Powers up volume control in display works but no audio sound hooked it back to the tv got sound through tv? is this amplifier problem in base module?

What system does it have ? Base or up level ,does it have a amp ? Do you know what a RPO code is ? Without testing no one could say for sure what the issue is . First off would need to know what system we are dealing with .
RPO Options
The entertainment system on this vehicle is configured with either a base or uplevel audio system. Both the base and uplevel audio systems contain a radio, antenna, and speakers.
The following shows the Enteratinment RPOs that are available for this vehicle:
• (UM7) AM/FM Stereo
• (U1C) AM/FM Stereo CD
• (US8) AM/FM Stereo, CD, MP3, RDS, EQ
• (US9) AM/FM Stereo, 6-Disc CD, MP3, RDS, EQ
• (UXQ4) Base Four Speaker
• (U79) Uplevel Four Speaker
• (WBM) Premium Audio
• (U2K) Digital Radio

Circuit Operation
Radio Power: The main radio power is supplied by the 10A RADIO (BATT1) fuse in the body control module (BCM). Radio switch-on power, 12 volts in ACC, RUN or RAP, is supplied by the 10A RADIO (ACC.) in the BCM.
Radio Grounds: The main radio ground provides a ground for the radio circuits. An additional braided ground strap provides a shielding radio case ground to reduce EMI noise. Both grounds are connected together inside the radio.
Radio Speaker Outputs: At zero volume, the plus (+) and minus (-) speaker outputs are both approximately 5-6 volts, measured to vehicle ground. If a plus or minus for any speaker output is shorted to ground or voltage, the radio circuitry will turn OFF all 4 speaker outputs for component protection. Above zero volume, the plus and minus change to create a voltage difference between each other, to drive the voice coil of the speaker.
Radio Park Lamp Input: The radio park lamp input allows the radio to sense when the vehicle parking lamps are ON. When the parking lamps are ON, this circuit goes to battery voltage, and the radio display back-lighting switches from full bright to the brightness level determined by the I/P illumination input.
Radio I/P Illumination Input: A pulse width modulated (PWM) voltage for instrument panel (I/P) illumination is provided to the radio I/P illumination input. The Radio uses this input to directly illuminate the radio buttons and adjust the radio display back-lighting when the park lamp input is ON.
Amplifier Power: The main amplifier power is provided by the 20A PREM AUDIO fuse in the instrument panel fuse block..
Amplifier Radio Speaker Inputs (WBM only): The radio speaker outputs, at a reduced output level for amplified systems, are the amplifier inputs. The amplifier boosts these inputs and outputs them to the vehicle speakers. Speaker plus and minus circuits from the radio change to create a voltage difference between each other. If one speaker plus or minus is open between the radio and the amplifier, the input to the amplifier is approximately half because only one of the circuits is changing. The speaker for that channel then operates at approximately only half the normal volume.
Amplifier Speaker Outputs (WBM only): At zero volume, the plus (+) and minus (-) speaker outputs are both approximately 5-6 volts, measured to vehicle ground. If a plus or minus for any speaker output is shorted to ground or voltage, the amplifier circuitry will turn OFF either the front outputs or rear outputs for component protection. Above zero volume, the plus and minus change to create a voltage difference between each other, to drive the voice coil of the speaker.
Amplifier Radio-On (WBM only): When the radio is ON, this circuit is pulled to 12 volts by the radio. The amplifier switches ON when this circuit is 12 volts and switches OFF when this signal is 0 volts.
Remote Radio Audio Signal Inputs (UE1 only): Audio output from the OnStar® communications module connects to the remote audio signal inputs of the radio. When the cellular telephone mute signal goes to 0 volts, the radio over-rides any other audio signal and uses these inputs as the source for output to the speakers.
Cellular Telephone Mute (UE1 only): The OnStar® communications module uses the cellular telephone mute signal circuit to over-ride the radio for OnStar® communication. When cellular telephone mute is not active, this circuit is held at 2 volts by the radio. When the cellular telephone mute signal is pulled to ground, the radio over-rides any other audio signal and uses the remote audio signals as the source for output to the speakers. If the radio was OFF when this circuit is pulled low, the radio will turn ON. Additionally, the radio fades the speakers to full front, adjusts the volume to an initial audible level, and sets an AutoTone designed for optimal use with OnStar®. When the mute signal is no longer pulled to ground, the radio returns to the mode it was in previously.

Hooking up a professional or factory scan tool that can read radio codes would be one of the first test's to do .
DTC B1025, B1035, B1045, or B1055 (w/out RPO WBM)
DTC B1025, B1035, B1045, or B1055 (w/ RPO WBM)
DTC B1030, B1040, B1050, or B1060 (w/ out RPO WBM)
DTC B1030, B1040, B1050, or B1060 (w/ RPO WBM)
DTC B1259
The following conditions are present for 250 ms or longer:
B1025 - B1055 01
One of the speaker positive output circuits is shorted to battery.
B1025 - B1055 02
The speaker positive output circuit is shorted to ground.
B1025 - B1055 04
The speaker positive output circuit is open.

Your best bet , take it to a qualified repair shop .

Here's the Manual
Good luck!
http://www.fixya.com/support/p168229-bose_lifestyle_sa_1_amplifier/manual-1542

Hi Suzanne, I want to help you with your question, but I need more information from you.
If you step back and look at this problem, there are two to three things that immediately come to mind: 1) have you hooked your headphone input to an output of another device like an amplifier or tv or ...? 2) Are you certain that the headphones are charged and the power to the base station is good 3) pairing the headphones to the base may be an issue.
Please clarify some things and anything else you can think of. Chad

I’m happy to assist further over the phone at https://www.6ya.com/expert/chad_65e28e99f5372e81

Try different inputs. Connect your output to a different amp to check there is a signal there. Sorry to suggest this but often it's a simple solution, check carefully that all controls - volume etc - are turned up enough. Check the two parts of the tower and where it connects to the base are connected properly

tried to hooked up a powered pc speaker in the earphone jack of your tv unit.then make an volume adjustment in the tv, if you can get sound there, the cause is will be worn out speaker or wiring connection. but if can get sound there their might have problem in the sound amplifier, check for bad audio amplifier ic or an open resistance in the audio section.

on most amp red isnt good that means it in protection mode try turning your setting on the amp down all the way and turn the volume down tell you can get sound out of them then turn up the volume to were you would to them most and set the to what sounds the best but make sure the light doesnt dim down when the base hits

Unless you have an external headphone amplifier, you need to use the headphone jack socket, if there is one. Some newer TV's allow for separate headphone volume and speaker volume control.
Have a look in your user manual.

The proper way to do this would be to use the audio output from the TV, either analogue left and right or the optical port, and send it into an dedicated amplifier or AV receiver. You can then use the amplifier or receiver to power the external speakers. If you are using a dedicated amplifier with no volume control you will want to change the audio output setting on the TV to "variable out" as oppose to its current "fixed out"settings. You can find this in the TV menu, usually under the audio settings. This will allow you to use the current TV remote to adjust the audio volume coming out of the external speakers.

You don't say what else works. Have you tried it with FM to eliminate external source causes? Does your TV get audio passed through to it? That would establish that there is program material to be amplified. Headphones work?

The following is from the User Guide -

Check to make sure that each speaker has been properly connected to the
speaker output jacks on the rear panel of the DCP501.
�� Check that the speakers are working by utilizing the Test Tone function as
described in the “Operation” section.
�� Verify that the DCP501 has not been placed in MUTE mode.
�� Check that the volume control on the DCP501 has been adjusted to an
appropriate listening volume.
�� Verify that the DCP501 is set to the correct source (CATV, VCR, DVD, Tape,
etc).
�� If the front panel displays O V E R L O A D , one of two things has happened:
1 If the DCP501 detects the speakers have a short circuit, it shuts down
the amplifiers. Switch the DCP501 off, remove the short circuit, and turn
the DCP501 back on. The DCP501 should now work as normal. If
O V E R L O A D is still displayed, a short circuit condition remains.
2 If the maximum amplifier output power is exceeded, the DCP501 shuts
down the amplifiers. Turn down the volume a little and switch the
DCP501 off and then switch the DCP501 back on and the DCP501
should now work as normal. If O V E R L O A D is still displayed, turn the
volume down some more.

The Speaker Setup menu has a Speaker Reset (to default settings) option.

Is your subwoofer amplified or passive?

You clearly understand that you need to use a variable line out to control the subwoofer volume via the TV. As the setup seems reasonable, I'm wondering if the subwoofer is getting a signal, but that it is at line-level and not internally amplified by the subwoofer speaker. Generally, if the subwoofer must be plugged into an AC socket in the wall, it has an internal amplifier and can be fed line-level audio. If it is "passive", it has no amplifier, and it must receive an amplified signal (over speaker wire) from an amplifier (or integrated receiver). TV's don't generally have connections to send out an amplified signal.

If the subwoofer is indeed amplified, then this is obviously not the problem, but it's the first thing to verify given the information provided.