Noise when it turns on

Is the sub dual voice coil?

here is the manual, I am looking for a more detailed version

Disconnect all speaker connections and rca cables. Leave power, ground and remote wires intact. Try turning on again. If you still have a protection light your amp is faulty. Hopefully you have warranty. Using an ohm meter to the sub will confirm whether its bad or not. Invest in a cheap test set of 6.5" speakers.
.A thumbs up would be greatly appreciated if this answer is helpful to you.

WE REPAIR THESE AMPS - EBAY - EDWARDS ELECTRONICS - :)

It can be the filter caps or the power amp module is going bad, read the service manuals:
http://manuals.harman.com/JBL/HOM/Service%20Manual/PB10%20sm.pdf
http://manuals.harman.com/JBL/HOM/Service%20Manual/PB12%20sm.pdf

I mod my pb-10/12, http://s807.photobucket.com/albums/yy352/budm/JBL%20PB-12%20mod/

More like to have bad Class D amp module, common problem with PB-10/12. I modified my, http://s807.photobucket.com/albums/yy352/budm/JBL%20PB-12%20mod/

Service manuals:
http://manuals.harman.com/JBL/HOM/Service%20Manual/PB10%20sm.pdf

http://manuals.harman.com/JBL/HOM/Service%20Manual/PB12%20sm.pdf

Make sure the subwoofer is set to low frequency, make sure subwoofer and bass are enabled on the headdeck. Make sure the gain is turned up on the amp, make sure the rcas haven't come out of the back of the head deck.

Pyramid makes the PB series of amps. I have one that's driving a Sub.
The PB 700 puts out rms 60watts x 2 @ 2ohms, which gives you some "headroom" for your speakers. You don't want to over drive speakers with , for example, a 1000 watts for 100 watt speakers, because that's a good way to blow your speakers.
There are many brands and models of amps that will fit your speakers. Just make sure the amp will drive 2ohm speakers, since your jbl's are rated at 2ohm impedance.
You may want to consider adding a Sub woofer to your setup. A single Sub would fill in the low end very nicely. If you got a 4 channel amp, then two channels will drive your jbl's, and you can bridge the other two channels to drive the Sub. That would be a kick'n sound!
Just make sure the amp is bridgeable
For example, the Pyramid PB 1200 is a 4 channel, bridgeable amp. This particular amp will drive the 2ohm jbl's, but you would want a 4 or 8 ohm Sub connected to the bridged channels.

There is a standby indication that activates after 10-15 minutes without any input signal. I suspect that might be what the red light is telling you - no signal.

Loud hum from a loosened cable is normal as hum usually means there's an ungrounded connection somewhere acting as an antenna and the amp is doing its job to amplify what it thinks is a signal, in this case 60hz stray ac current is being sensed nearby. It's a good sign that you get hum from the sub because that means the amp is alive.

Avoid manipulating cable connections with the Sub or Receiver turned on as you could introduce a static spike that could harm any connected equipment.

Are you certain a bass signal is making it into the sub? The complexities of modern AV receivers vary in how you configure them to direct LFE to a sub. Bone up on that end of the chain.

Or, just hang a CD player on the Inputs of the sub and play something with a reassonable amount of Low Frequencies.

>>>> Be advised that this way of testing has NO VOLUME CONTROL because amps without volume controls always operate at maximum gain, relying on your external controls to attentuate it (hence, the loud hum from a loose cable); so choose a track that eases into the loud parts with some quiet parts up front and BE READY TO PAUSE THE PROGRAM AT ANY SIGNS OF STRESS. <<<<

A living sub will produce only muffled rumble in the absence of other speakers producing the higher frequencies which carry the intelligence of the signal. If that works, back to the receiver for settings. If not... sigh.

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For hum problems, even those you cause yourself:

Disconnect all inputs to see if that helps. If it goes away start with the signal cables and add in things until it comes back.

Sometimes the reversing the orientation of the AC plug can help with hum. Or it could be something like a loose or high resistance connection internal to the sub. Good luck.

There is actually some good news.  I had this problem with my PB10s (1 have 2 PB10s and 2 PB12s) It is one of 2 things, the first is that it could be a capacitor and resister combination on the amplifier board (which was the fix for our PB10 with the same problem), or 2nd, the AMP IC, which is not available for the PB12. hmmm