My HP ze4530 (purchased November 2003) won't turn on. I push the power button, and it lights up for a split second and then goes off. It will start to turn itself on for a whil, but no luck. Can I buy a part or something to fix it? (I have heard that it may have overheated, which would cause this failure.)

Sounds like something is fried, but it will take a tech to test the machine and see what. Since its not likely to still be under warranty (unless you purchased and extended warranty), your best bet is bringing it to a technician to check it out and give you an estimate.