Welcome, Newcomer. Start with our troubleshooting guide. Click on the link in my signature, and work through every step in the guide. Don't skip anything, just because you think it's irrelevant. Also, if need be, utilize jsc's guide to breadboarding (it's a link in the troubleshooting guide).
I finished the troubleshooting guide and the computer still doesn't work. But when I took everything out of the case and put it all together the power would turn on in intervals. Then I tried jumping the PS by itself and the fan spun to life and it didn't stop. So then I tried it with just the hard drive and the CD drive and it turned on in intervals again. So does this mean that the problem is with the PS?
Possibly. You see, the paperclip test doesn't really prove much. The PSU has two roles:
1. Convert AC into DC, which your computer parts need; and
2. Distributes power to the connnected components on demand
The paperclip test can be very misleading, in that the result can be a false positive. Though the AC to DC is aparent (PSU fan spinning), that doesn't mean that it is supplying the rest of the computer with adequate power.
On the other hand, when you breadboarded, how did you turn on the power to the mobo? Did you use the case power button, the mobo power button (if available), or did you jump the PWR_SW pins?
I did what you said but the power supply is still going on intervals so the MB can't finish the beep patterns, but this is the first time it actually beeps, so it's making some progress. I got to the RAM stage but couldn't hear the whole beep pattern the only beep I heard was one long beep, but after the beep the PS stopped then started its intervals again. Could the problem be with both the RAM and the PSU?
At this point, I believe the PSU or CPU is the problem, but if you want to try reducing the load on your PSU, leave mobo out of the case; install CPU and HSF. Jump the PWR_SW pins again. If the power stays on long enough, you should hear the "no RAM" error beeps. If power is stable, install one stick of RAM (check your mobo manual for single stick placement).
If you can get your hands on on a digital multimeter, test the PSU P1 connector. This is the 20/24-pin connector that is the main power supplier to the mobo. This may be annoying because you can't get the power to stay on with stability. Just each non-black-colored wire. The voltages should be as follows:
Red = +5V
Yellow = +12V
Orange = +3.3V
Green = +5V
Brown = +3.3V
Blue = -12V
Gray should go from 0V to 5V when you turn on the power
Keep in mind that the acceptable tolerance to these values is 5-10%. If your PSU voltages are below acceptable levels, replace it. If PSU voltages are OK, then the problem is likely mobo or CPU. I would RMA them both at the same time. Just tell the CPU tech supprt that you've already replaced the mobo and the PSU checks out fine. Do the same for the mobo tech support, but tell them you've already replaced CPU.