By "keeps trying to" do you mean it comes on, then shuts off right away, only to come on again and shut off, over and over?
First, look at the Motherboard and see if there is any blown capacitors.
Second, test the Power Supply to see if it is still good.
Third, try removing the RAM and using a known good stick of RAM.
Fourth, try removing any cards that are plugged into your PCI or PCI-E slots.
Thats what I can think of off the top of my head.