If you have swapped the power supply then the issue is your motherboard.

but have to ask is the fan and LED's on the case lighting up?

if not it is your power supply.

If they are then it could be several things
1. the motherboard is encountering a fault could be bad memory could be a bad video card or the processor may be bad.

This is one of those where you have to ask yourself what do I want to salvage and at what cost?

power supplies are cheap $20 to $80
motherboards not so much $100
processors really not worth upgrading as a good one is around $200

Here is how I look at it
If you have a P4 (Pentuim D} that is less than 3.0GHZ its not worth fixing. Unless you have someone who knows how to diagnose the labor rate will get out of control 3 hours of labor and ANY part add up to the cost of a new computer.

Save what you can
items such as newer DVD burners, hard drives or gaming video cards can be transferred to a new computer.

my recommendation
A. check weekly ads for a pre built FRY's has good deals if you have one in your area
B. Ebay is a good source for computers off corporate lease if you have a copy of Windows XP find one that has a XP certificate sticker ON THE UNIT.
or find a seller who sells them with windows pre loaded this also REQUIRES that the computer has a windows COA sticker on it.
C. check craigslist people upgrade and they usually pop up for under $150 once again make sure the copy of windows comes with the COA.

Hope that helps