TV turns itself off after a few seconds, no picture at all
As far as fixing goes, you might as well get a new TV... Unless its a LARGE EXPENSIVE HOLY $%^# TV, It will cost more to fix, than to just buy a new one, unless its under warranty, which being an older model as that (or so im reading) It may not be covered.
Try unplugging the TV, and while unplugged, hold down the power button for a full minute (yes, with the plug NOT in the wall) after a minute, plug it back in, and try. Its a hard reset. If it still does not work, and you've tried different outlets, It's probably a repair issue, and you'll need to get someone to fix it, or just junk it :-/