Was it stored somewhere cold? This may not be the issue yours had, but when electrolytic capacitors start to fail they are worse when cold, the ESR drops as they warm up. This is the reason so many devices will work fine then you turn them off and the next time you try to use them they won't turn on. Capacitors may bulge or leak when they get really bad but it's quite common that they look perfectly fine.
No, it was stored in the living room of my apartment, so normal temps. It just sat there for a few years, unplugged and untouched. When I was hooking it up, the base had become stuck to the glass table it sits on because it hadn't been moved in so long!
I have a Dynex 32" that my son gave me instead of putting it on the curb. It has no sound but works as a decent computer monitor. The reality of it is that if it stopped working, I wouldn't waste time trying to repair it unless it was obvious bad caps. It is a low quality product, but for the price I got it for, it serves my needs.
Funny, I got mine for free too. And I feel the same way - if I didn't find anything obviously wrong, I was going to trash it and buy another one for $100 or so. But it was annoying because I never use a TV anyway, and I only wanted it to set up a raspberry pi I just got. Once I have it set up and networked, I don't need a monitor any more because I can use ssh. So I wasn't looking forward to buying a new TV for 30 minutes of use!