Connect from wall cable to tv.

Polaroid FLM 3701 User Manual Page 10
Here is the manual

It looks like your power supply might not be providing enough current to get the LCD to power up. This LCD needs about 3 to 4 amps to work properly.

Unfortunately modern televisions and monitors are full of electronic semiconductors of which many are likely have got destroyed along with your original power supply during the storm. A nearby lightning strike will send high voltage spikes down aerial cables as well as through socket outlets.
If you have contents insurance you should be able to claim for a new monitor.

No because it is a monitor only; meaning it does not have a TV tuner of its own.

It may have dying power supply due to bad caps, this is common problem with 3+years TV and monitors.
Please see my basic troubleshooting guide here:
http://www.fixya.com/support/r5093881-lcd_flat_panel_tv_troubleshooting_guide
http://www.fixya.com/support/r6150077-basic_lcd_monitors_troubleshooting
Failed TV and Monitors: http://s807.photobucket.com/albums/yy352/budm/
Learn about bad caps: http://en.wikipedia.org/wiki/Capacitor_plague
Parts: www.shopjimmy.com
Capacitors kit: http://lcdalternatives.auctivacommerce.com/Default.aspx he can make you a set of caps.
Or www.digikey.com just make sure to use caps with low ESR, 105c, high ripple current, long life rating such as PANASONIC FM or FC series.

Having browsed the user manual I wonder if you plugged in the Sony BDV T57 Home Theatre System while the Polaroid FLM-2632 tv was powered down via the optical cable .
Then powered up the Sony BDV T57 Home Theatre System first and then powered up the Polaroid FLM-2632 tv
Maybe the Polaroid FLM-2632 TV has to detect that the Sony BDV T57 Home Theatre System is connected and powered up when the Polaroid FLM-2632 powers up. To activate its digital audio out ????
The note part about only being available only under HDTV (cable/air) mode. Might be the cause of your hassle also ?


DIRECTLY FROM THE USER MANUAL
source from
http://tv.manualsonline.com/manuals/mfg/polaroid/polaroid_flm_flm2632.html
"
? Connecting to Audio Receiver:
Use an audio cable to connect the audio receiver's audio LINE IN jacks to LCD TV's
AUDIO OUT jacks. ? Connecting to Digital 5.1 Sound System:
METHOD A:
Use an optical cable to connect the audio amplifier's OPTICAL IN jacks to LCD TV's
OPTICAL OUT jacks.
METHOD B:
Use a coaxial cable to connect the audio amplifier's COAXIAL IN jacks to LCD TV's
COAXIAL OUT jacks.
Note: Above mentioned function is only available under HDTV (cable/air) mode.
? Connect all AC power sources, before turning on the power switch of the LCD TV or
other connected equipment.
? Press the button on the remote to turn on the LCD TV."

In the Polaroid FLH-3701, the fuse is located on the power supply board, next to the AC power connector. It is a small black cylinder. It is labelled F1. Value is 5 amp, 250 volts.
A fuse does not blow for no reason. Most commonly a fuse will fail because of a short someplace on the board. I have this same TV. The fuse blew. The reason was transistor Q6 had shorted. There are two identical paired transistors on the output side. Q6 and Q7. They are both Infineon 11N60C3 MOSFET transistors. Check those for a short. There may be a burnt smell.
More commonly, this TV will fail because of bad capacitors on the power supply board.

Expensive!
http://www.technotronic-dimensions.com/Products1.html
Cheap but not in stock.
http://tv-part.com/index.php?target=products&product_id=768
Try fixing it?

Hello, the HDTV input is what you would use if you were not using a cable box.
You should connect your cable from the wall to coaxial input on the cable box, and connect an hdmi cable from the hdmi output on the cable box to the hdmi 1 input on your tv and then switch the tv to that input.
Tommy, HD Installations

I googled this a bit and found the sound going out is a normal problem , if under warranty still call polaroid
here is the service manual
http://pettersservice.com/polaroid/docs/FLM-Series-26-32-37-ServiceManualFinalNA_20070418.pdf

looks like its a chip on the output of the video ad board.
or since the sound was terrible anyway get a surround sound speakers and connect them to your cable box, no cable box then you will have to have it fixed.