New (less than 1yr old) 32" LCD TV: Model# NS-LCD32-09: No sound. Have tried everything according to manual troubleshooting guide, nothing works. Had Cable company reboot, to no avail.

See troubleshooting section of manual on page 20

Setting Up Your Tv; Maintenance; Troubleshooting - Insignia NS-50DF710NA21 User Manual [Page 20] ' ManualsLib

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User manual Insignia NS-65DF710NA21 (English - 28 pages)

The first thing I would try is to disconnect the tv from the power source. Wait five minutes before plugging it back into the wall socket. Turn the tv back on and see if you get a display. Try changing the channel and switching inputs. See if you can get it to display anything at all. You could shine a flashlight at the screen and see if you can make out an image. If you see an image with a flashlight then your backlight is out.

Is your tv less than a year old? If it is less than a year old you are still under the manufacturer's warranty. I would see if Best Buy would honor the manufacturer's warranty in store. If that is not the case they should give you a number to contact Insignia directly.

If your tv is out of warranty, it may be cheaper to replace it. I would do your homework and check the price of a repair vs the price of a new tv.

You can download the setup guide and user manual from the link below
Insignia 32 inch Class 1080p 60Hz LCD HDTV Blu ray Disc Combo

IT MAY BE YOUR AUDIO/VIDEO CORD

That sounds correct, the main board is bad (the backlights ON signal is stuck low so it will not turn on the backlights board) and no way the repair shop will have the proper tools to do delicate surface mounted repair works. Mian board is not cheap, I would sell parts on EBAY nad spend the money on new TV.
I have seen less thane two years old TVs that go bad already, they do not make it to last.
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
http://www.fixya.com/support/r7406380-tv_training_manuals
Failed TV and Monitors pictures: 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.

ebay.com

Service manual; http://www.my.electronicshelponline.com/uploads/Insignia_Xoceco_LC-37HV41_NS-LCD37HD-09_LCD_TV_SM.pdf

Power supply is only $32.
http://bestbuy.partsearch.com/Model/Best Buy Company Incorporated/Insignia/NSLCD37HD09.aspx?SearchTerm=True

http://s807.photobucket.com/albums/yy352/budm/Insignia NS-LCD37HD-09/

Please see my basic troubleshooting guide here:
http://www.fixya.com/support/r5093881-lcd_flat_panel_tv_troubleshooting_guide

Failed TV and Monitors: http://s807.photobucket.com/home/budm/allalbums

check the invertor boards resistors they power the back lights
also check for any capactors that have blown (raised tops) they look little bateries

if you have dvd player then connect its audio out to your tv audio in. if no sound then, it might be that your audio amplifier inside your tv is the culprit. usually this happens when turning the volume fully.

If under warrenty then call vizio!
I believe its sound board but I could be wrong.
No easy fix, the part is 220$ service is 210 a used LIKE NEW 42-50 inch is 500$ shipped !
Sorry to say this but it happened to my 50 inch just before I heard a pop then it would not show a picture and had no sound.
Call them up if your tv is less then 1 yr old!