My Toshiba Portege M200 won't start, overheated?

Hi,

Some time ago, I was using my Toshiba Portege M200. I was mostly using my comp running photoshop, a browser, Trillian, and uTorrent and not much else.
As per usual, it would get really hot on the underside (like almost burning up), but I never blocked the fan or the opening on the sides etc. But one day, I was just using it, and it got really hot, and then it shut itself off. Well, I tried to turn it on again but after several attempts, nothing happened.

I waited like about half an hour or more, and tried switching in on. It started, as in i could hear the harddisk running or starting up, but the screen gave some funny colours like some pink blotches or what not, and then it died. And since then, I couldn't make it run anymore.

When I plug in the AC adaptor, i can see the adaptor light on. When I switch on the power, I can see the power light on, except the pc makes no sound. So the harddisk, or nothing, is running at all.

Also, the digitizer stopped working or was semi faulty, as in some parts of the screen i couldnt draw on with the pen, but thats been for a while now.

So a few questions

a) Is there anyway I can know which component died, and how much would it cost to fix it (its not under warrantee anymore, and the toshiba repair centre was like gonna charge 50euros just for the examination or something, so if its an expensive part i won't get it fixed.

b) does this have anything to do with the AC adaptor because the first time i couldnt start my Toshiba it was because the AC adaptor was faulty...

Bonus question: Do Toshibas overheat alot, because while I look through forums about my comps problem, i tend to find stuff about people complaining about dust in the fan of the heatsink, or etc.

Thanks!