Need some PC help

I know....double post......

The Alienware laptop I got my wife almost 3 years ago has decided to play dead.....or is dead, I can't really tell the difference.

here is what it does;

I push the power button, the "power on" light turns on.

if I leave it on this way for an extended period of time, the bottom gets hot and the fan turns on.

if I put in a CD, it will spin it, act like its reading something, but will not give any indication that it is running.

Here is what it doesn't do;

the hard drive does not spin.

the screen does not turn on (not just blank screen but "the computer is turned off" kind of dark

it does not play any start up sound to suggest that the problem is with the screen alone.

On one occasion it did actually start up, the screen lit, but only displayed a partial and very garbled "do you want to start up in safe mode" screen.

I'd love to have it fixed by the time we go to the LAN and if I send it out for repairs, that is not likly to happen (nor will we be able afford to go to the LAN if it gets too expensive) but, I have built computers and if I knew what was wrong I am confitdant in my abilities to fix it (provided it is not a software issue, or something that would require tons of diognostic tools that I do not have) so if anyone has any suggestions on where to start, I'd be very appreciative.