Since you reinstalled Windows on a new hard drive this should rule out software as the problem. Perhaps you have a bad memory card or a bad connection with the memory. I would remove and reinsert the memory to see if this helps. You could also try running with only one memory module, this can pin-point the problem.
You might also read the Event Viewer System error log. You go to Control Panel - Administrative Tools - Computer Management - Event Viewer - System. Not everything you see here is a critical error. But, you might see the hardware error.
Another tool is to Disable Automatic Reboot on Error
If you are suffering from the BSOD (Blue Screen Of Death) the PC stops due to the stop error and then, in default configuration, automatically reboots.
Chances are good that you want to know what is going wrong and how to fix the stop errors. Well, you can't just say "It's rebooting, what's wrong." With that little bit of information no one will be able to help you fix it. Instead we need to know the "stop error" and the exact wording for the reason that it stopped so that we can diagnose the problem. Then, and only then, will we have enough information to help solve your problem.
Older operating systems used to do it nicely and just plain stop... Now? Now it reboots for you because that is generally easier than it is to worry about the problem. Let's stop that shall we? It would make it easier for all of us if we could know the exact error message after all...
Click the Start button
In the System Properties window click the Advanced tab
In the Startup and Recovery area click the Settings button
In the Startup and Recovery window UNcheck "Automatically Restart" (in the System Failure area)
Click OK and then click OK again
Then when the PC crashes, make note of the stop error and related information
I hope you find the problem. Good Luck
Thanks to xpcman for this tip on the forum.