You need to isolate the problem and it can be done by doing the following:

Disconnect the power cable to the power supply.
Remove the cover to the pc and disconnect ALL devices that are connected to the power supply then disconnect ALL data cables connecting ROMs, hard disk drives and floppy disk drives to the motherboard. If you have any peripheral cards in the pc remove these also.
Reconnect the power cable and turn on the pc. If you get the same result look closely at the cpu fan and heatsink assembly, sometimes the the part that holds the assembly against the CPU can break and the heatsink is no longer touching or only partially contacting the CPU. Also make sure that all power cables to the motherboard are firmly attached. If all appears normal with the fan/heatsink then borrow a power supply and test with that.

If the pc turns on then disconnect the power again and begin reconnecting all that you disconnected earlier but do this one item at a time. ie reconnect the power and data cables to the hard disk drive, turn the pc on. Continue in this fashion until you get the symptoms you've described and you will have identified the faulty part.

Good luck.

what if the heatsink is gone? I tested the power supply with a different one at the same thing happen. it turns off then turns right back off. I took the cooling fin off the cpu there was hardly any heatsink of it and it looks like it was taken off befor.

Heat problem - get some thermal paste and put between heatsink and cpu. Make sure you don't overdo the paste, though - none should come squishing out when you reattach the heatsink and fan. Another problem may be that the fan on the heatsink is not turning fast enough, thereby not helping to dissapate the heat from the cpu. In that case, purchase a new fan and/or heatsink-fan combo.

If a known working power supply produces the same results as your power supply then you need to go through the procedure I outlined for you in my previous post. It is imperative that you eliminate the other parts of the system, however, if the heatsink and fan are visibly NOT contacting the CPU properly then you probably need to replace them.

if i use the paste do i put it on the heat sink then attach the cpu then connect all of them to the cpu socket?

I agree with bfdman -that the source needs to be isolated, however if you have already separated the cpu and heatsink you do need to re-apply a bit of thermal paste. I get the idea that you are calling the heatsink the thermal paste itself, as you referred to "fins" - which is actually the heatsink. or mabe I am just confused. The thermal paste can be purchased at Radio Shak or a similar store

yes, put the paste on the heatsink, attach cpu - you said this was an older computer - does the heatsink have a fan or not? I have worked with some that have no fans attached, but the process is similar, except there is no fan to go with the heatsink. Make sure you replace the cpu in the socket very carefully so as not to bend any of the pins.

When i put a working power supply in the computer i had nothing attach to the motherboard and it did the same thing with think attach to it. It would turn on for 5 seconds then turn off. That was with nothing attached.

Actually I have depending on the configuration of the socket itself, attached the cpu first, then the paste and then the heatsink. Sometimes much easier to attach the cpu first, and sometimes have to attach the heatsink to the cpu and then into the socket. Either way just be careful of your pins and not too much paste - too much is just as bad as not enough