Unfortunately, diagnosing and addressing this problem will be a tedious, time-consuming, methodical tasks. You cannot jump straight to Windows and play games if you want to diagnose this problem. Prime95 is by no means the best way to check RAM stability. I wrote this earlier today for a RAM diagnosis problem. Sorry if it only 90% applies to you.
Step 1) What is the make and model of your PSU? If you're in Windows, install and run HWMonitor and tell me all the voltages it gives you (3.3V, 5V, +12V, -12V, CPU). If you're not in Windows, go to your Bios and look at the Hardware Status or Health menu and tell me what voltages it reads out. I doubt this is your problem, but always start at the PSU.
Step 2) Install Memtest86+ to a flash stick. Power off your computer and disconnect your hard drive so you don't waste time accidentally booting Windows.
Step 3) Since you think RAM is the problem... Remove all sticks except for 1 and cycle it through all the RAM slots on your board and see if it posts consistently with any of the slots. I had a motherboard where the first two slots had to be set slower than the other two. Repeat with all your other RAM sticks to determine if any configuration posts consistently. If not, then it's less likely that it's the RAM. (Do not connect your hard drive). Only connect 1 stick in whichever slot works best.
Step 4) When you do get your computer to POST, go to your Bios and load defaults. Change your RAM to 1066MHz and 9-9-9-30 timings w/ 1.65V or whatever the RAM reads on it. Save and Exit and boot to your flash stick. Run through at least 1 cycle of Memtest86+, two would be better. Swap your RAM sticks and repeat Memtest86+. Put in all your RAM and repeat Memtest86+. If you pass two complete Memtest86+ run throughs without seeing any errors such as freezes or error messages (should take about 30 min per run through), your RAM is not the problem.
Step 5) Does your computer consistently POST? With whichever RAM sticks and slots that work connected and set to 1066MHz 9-9-9-30 (Auto on all the rest), enter your bios. Check that your CPU speed and voltages are set to manufacturer defaults (Intel has a helpful webpage for every CPU). Connect your hard drive and boot Windows.
Step 6) In Windows, start HWMonitor. Keep an eye on voltages because they shouldn't fluctuate much at all. Tell me your idle CPU temp. Now run LinX on a problem size of 10000 for 3 loops. Did it freeze, BSOD, crash, or return errors? Stop LinX if you exceed max temps specified by Intel (go with 70C for C2D, 80C for Nehalem). Did it freeze or crash? If your temps don't get too hot, run LinX for 20 loops and see if it gets errors. If not, then it's not your CPU or RAM.
Step 7) Install MSI Afterburner with Kombustor or install Furmark. Run Kombustor/Furmark, monitoring your GPU temps. Do you get errors. If so, download new drivers and perform a custom "Clean Install". Check your device manager (after a restart) to see if there is any software lacking drivers. Attempt to describe your restarts. At this point (if nothing else was erring out, it's VERY likely that it's a bad PSU. Alternatively, it may be a bad mobo. RMA one of them.
Please report any unusual errors or stumbling blocks in the above processes.