This is a long story. I am not very good at summarizing things, so please excuse its length.

I am in the process of moving my house from Windows to Linux. Unfortunately, at this time, my desktop is acting as a media center PC for my entire house and my homes' use of Windows Media Center is something I had planned to expand going forward. The killer application of Media Center is the fact that it is possible to purchase Media Center extenders to be able to use it remotely like a set-top box, which is something that has no Linux alternative and since good tuners use PCI/PCI-Express, it is not possible to virtualize the server.

Because of this, I built a new PC to act as a media center server for my house. I used some more components from newegg (case, motherboard) with some some parts I had lying around the house (everything else) to build it. Initially, I was able to boot it, but it would quickly freeze in the BIOS and this made the system unusable. I then did an RMA with newegg and newegg replaced the motherboard. I reassembled the system and promptly after plugging it into an outlet and turning it on, I discovered that it would immediately turn itself off:

Here are the system specifications:

Intel Core 2 Duo E6300
4GB of RAM (2x Corsair VS2GBKIT667D2)
XFX GeForce 9300 Motherboard
320GB Western Digital Caviar SATA hard drive
Plextor SATA DVD-Burner
Antec P180 Mini Case
Antec Phantom 500W PSU

The Antec Phantom 500W PSU is actually a unit I received as a replacement for an Antec Phantom 350W PSU that died on me after like 18 months. It had been in the basement for years and was new in box when I pulled it out.

Everything appears to be properly connected, with the CPU, the CPU fan, the RAM and all of the various power cables being installed properly. Could current underflow protection be causing this? If not, does anyone have any idea what else might be causing this?

You could test that the PSU is actually working by using a PSU tester, or for nothing via the paperclip trick. If it is working then what is possibly happening is that the start up power surge is triggering the thermal cut-out in the power supply. This is because it is being seen as a short rather than a surge. A factor in this may be that the thermal cut-out is necessarily set to trigger at a lower level than it would in a conventional PSU.

You had a collection of parts that didn't work right. You changed one of the parts and it still doesn't work right, so assume that the part you changed wasn't the bad part to begin with.

The computer would never booted into the BIOS if the PS or CPU had hard faults. RAM is usually the hardware culprit for unstable systems. Try using one stick of RAM in each socket until the PC boots into the BIOS. If the first stick won't boot in any socket try the other. (Keep the HD and optical drive disconnected while doing this, the fewer the number of variables, the better. )

If there's still no joy, try connection the PS to a working system. This won't take long because you don't even have to put it in the case.

That should keep you busy for a while, so came back when you're done.

The parts were mostly working pulls from another system I have that I had been upgrading incrementally over time. The RAM I actually removed from my desktop when I assumed this system. I took the opportunity to go from 4x1GB to 2x2GB, with an upgrade to 8GB planned in the future.

Anyway, I will assume that the previous motherboard could have killed one of the sticks and try experimenting with them. If that does not get it to start (without turning off within 1 second of starting), I will try a new PSU. I do not want to put the PSU in my desktop if there is a chance it might damage it. Does anyone have any suggestions on where I can get a low cost PSU that would definitely not run the risk of possibly tripping current underflow protection in my system? If the RAM turns out not to be the case, I would like the PSU I buy to be a Seasonic PSU.

you didn't mention if there were any beeps? look up the failure codes for the beeps in the mb manual.

unplug all drives, everything except video, cpu, and ram... see if it boots then.

try to do cmos reset on the motherboard, using the cmos jumper... make sure that the cmos jumper is not in the shorted-out position when trying to turn on the pc.