Well there are two options here and unfortunately there's no easy way to tell which is which without opening the TV.
First and actually more common option is failed power supply. It fails in a way that allows it to power the basic TV functionality (main board works, you can power on and off), but it fails to provide power to the backlight so that you can see the display.
If you like digging you can open the back cover and use a voltmeter to figure if both power cables going out of the power board provide 24V . One of the goes to the main board and the power is there in your case (since you can turn on/off and can hear sound), the othe goes through a connector to the LCD's backlight. That's the one you suspect has failed and that's the one you should measure.
if you can see 24V there then it is NOT the power board.
If you do not have 24V there then IT IS the power board. You can have yours serviced or buy a replacement.
See
http://blog.coppelltvrepair.com/2010/04/polaroid-flm-3232-power-board-r0804.html or seek around to just buy a replacement.
Now, if it isn't the power board, it might be the inverter that takes that power. Inverter is a bit harder to troubleshoot on this TV model and I will not coever it here.
Finally, there is a minimal risk that this might be due to overheated and malfunctioning main board. Replacement is the only viable alternative here.
Hope this helps!
Bobby
www.coppelltvrepair.com
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