It is normal during the install of windows for the screen to go black for a min or two. Is this what you are seeing or does the system reboot itself? If it is rebooting, here are some items to check.
Board posts however there are lockups, bsod, cannot install windows
1) Since it posts, check your temps in the bios. It is very difficult to say what a "Normal" temp should be since each type of cpu [P4, Athlon, AMD64, etc] has a normal temp. What you should see in the bios is a stable temp of <55C. If the temp is much higher than that, you probably have the heatsink fan installed incorrectly.
2) If the temps are ok, pull all cards from the system except the video card. Disconnect any peripherals such as printer, scanner, usb hub, etc. Is it stable now? If so you have a problem with a piece of hardware or its driver.
3) Test the memory with a tester like memtest86. Just because you see a memory test during post means nothing. All that does is check to see if the memory is there. It does not check each memory address. Note this test is run from bootable media ie CD or floppy; there is no need for an operating system to be installed.
4) Power supply. A modern P4 or AMD64 needs a quality power supply. It is difficult to say what wattage you will need since this is dependant on many things; the number of fans, the number of hard drives you have installed, the type of video card you have installed, amount of ram, etc. A bare minimum would be in the neighborhood of 350W. The power supplies that come with many cases [however not all] are junk. Since modern systems make a very high demand on the 12V rail of the power supply, what you are looking for is something around 20+ amps on the 12V rail. Some good brands of power supplies are Antec, Enermax, Enlight, Sparkle, and some models of Coolmax. There are other quality units, however those are what I use in my builds.