If the system has issues booting with 4 sticks of ram, but not 2 sticks of ram, it's most likely one of the following.
1) The second set of ram dimms is damaged.
2) The second set of ram dimm SLOTS are damaged.
3) There is not sufficient power to power all ram slots (unlikely).
First thing I would check...is if all the ram dimms are from the same company, with the same voltage and timing specifications.
After getting that information, I'd go into the bios, and make sure all the timing and voltage settings were properly set. Do not assume the bios will correctly set voltages, most of the time it WILL NOT. It will default to the 1.8v (DDR2). Many ram dimms which run faster timings (such as 4-4-4-12) require higher voltages to obtain it. (example, 2.1v).
If you never set either the timing, nor the voltage in the bios, the ram will run out of spec. Since each ram dimm has it's own tolerances, the first few dimms might be fast enough to handle higher speeds at lower voltages, but the second set might not.
Now if all the settings are correct, I'd run a memtest.
http://www.memtest86.com
(That link seems down, try this one instead)
http://www.memtest.org/#downiso
Burn to disk (get the iso) then boot to the cd. Allow it to run. If you get memory errors AND your memory settings are correct, then return the ram for replacement. I'd test in sets of 2, then in sets of 4.
If you don't feel like listening to me, and you just decide to reinstall windows...here's a secret IT tip.
If you get ANY copy error (where you have to tell the installer to retry) during the windows installation, that's 99.9% of the time a RAM ERROR. So then just go ahead and follow my instructions again.
If you wonder what type of ram I usually run, it's always muskin.
http://www.newegg.com/Product/Product.aspx?Item=N82E16820146731
This is my current favorite DDR2 set.
5-4-4-12 at 1.8v, allowing it to run in systems with bios's that can't modify dimm voltages.