The tv turns on and digital tv comes up on the bottom of the screen, and then it shuts itself off by itself. We have unplugged it for a few minutes to try to reset, but it continues to do the same thing?

I had a similar problem with my Phillips 42 in. LCD HD TV.

Here's the problem. The Power Supply Board. I opened my TV up(warranty was up of course) and found several bad capacitors. Phillips and several other companies were sold capacitors that although were highly rated failed within 5 years because of a lack of preservatives. All sorts of electronic equipment is now being effected due to these defective capacitors.
Solutions?
1. Take it in and have it fixed
2. Open it up, check the board for faulty capacitors(bulged or leaking) Buy a new Power supply board and install it.
3. Remove PSB, remove faulty capacitors and replace with compatible new ones.

Hope this helps