I have probably used the Playstation less than 10 times to play games and less than 10 times to watch movies.
Sorry to hear that you're not enjoying your PS2. I'm really abusing mine. I sometimes drag it along when I travel too.
I am a fairly big gamer and have been using my PS2 at least twice a week for gaming sessions (I also use a PS2 at work nearly every day to play games during my lunch hour) and have found myself moving it into the bedroom for DVD playback far more than I ever expected to (I far prefer watching movies on my stand-alone DVD player and THX home theater system, but sometimes my wife and I just like watching movies and especially the extra features from the comfort of our bed).
Now it will no longer turn on/power up.
I bought mine for $299 during launch week and have had absolutely no problems. Can't say I've ever heard of problems with a PS2 not powering up...perhaps it's just the cable. If you have other Sony products (like a Handycam or a Cybershot camera), you could try using one of their power cords (a lot of Sony devices use the same cord between the transformer and the wall).
That said, I certainly had interesting problems with my original first generation PlayStation. Like many early adopters, I had problems with it overheating (turning it upside down helped, but after awhile it would hang when playing video, hitch during streaming audio, and eventually fail to boot games). That said, on occasion I can still "jump start" games by opening the lid, pressing the button, and spinning the disc. I got a second PlayStation when the price dropped which has had none of the problems my first had. Of course, I have little reason to use the PSX nowadays since the PS2 plays PSX games.
Playstations only have 90 days warranties. What's up with that?
I could be wrong, but I think most video game consoles only offer 90 day warranties.