How can I fix my 12 inch kitchen LCD HDTV/DVD Combo?

I have an Audiovox 12" Kitchen LCD HDTV/DVD Combo, M/N: KLV 3913, mfg., Oct. 2008, purchased from Wal-Mart about 8 months ago. About 4 months ago, while using the TV, there was a sound like an electrical "pop", then the screen went black and the sound stopped. The AM/FM, DVD and volume all work well, and occasionally the TV will come on, sometimes go black losing sound with it; other times the TV may stay on a little while, often with sound static, then shut down. Most times the TV will not come on at all. It is mounted under the cabinet and has cable TV service. The electrical outlet has been tested fine. It is protected by a surge protector.
To return to "factory" seems rather shady. It will cost as much as the TV cost ($300). Also, the "factory" does not guarantee repair or replacement nor a warranty if you do get a repair or replacement, and I am asked to pay shipping both ways. What we've read online from other purchaser's, the TV part of this appliance has a history of this (blacking out); we knew that upon purchase, but it had the largest picture size and we really wanted it, so we took the risk.
Help would be appreciated if there is a "home" or "DIY" repair. Also, we cannot locate TV repair shops in our region or retired, work-at-home, repairmen who advertise.
If there is other needed information, I'll try to answer any questions. Thanks in advance.