Windows 7 Ultimate 64 Freezes during several instances

Do you get a BSOD or a mini dump file? Or is it just a freeze? If you have mini dump files, please upload them. Off the top, I suspect video drivers. You may to to experiment with the drivers to find the one that works best on your system.

So it doesn't crash, it just freezes up. Does it ever unfreeze and continue working, or do you have to restart the machine to get functionality back?

OK - do you have a PS/2 keyboard that you could attach to the system temporarily (if you don't already use one)? There is a fairly quick way to test for hardware problems, but it requires a PS/2 keyboard to work properly:

1. Create or set the following registry value:
Key: HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\i8042prt\Parameters
Value: CrashOnCtrlScroll
Type: REG_DWORD
Data: 1

2. Right-Click on the "My Computer" icon on the desktop and select "Properties", then click the "Advanced tab. On the "Advanced" tab, click "Settings" under the "Performance" header. Click the "Advanced" tab, then click "Change" under "Virtual Memory". Set the pagefile to be located on the partition where the OS is installed, and set it to be equal to Physical RAM + 50 MB.

3. Also in the "System Properties" window on the "Advanced" tab, click the "Settings" buttun under the "Startup and Recovery" header. Make sure "Complete Memory Dump" is selected (see 3a if this is not in the list). You can change the location of the memory dump file to a different local partition if you do not have enough room on the partition where the OS is installed.

3a. If the "Complete Memory Dump" option in step 3 is not available, you will need to manually set this registry value:

Key: HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\CrashControl
Value: CrashDumpEnabled
Type: REG_DWORD
Value: 1

4. You will need to reboot for these changes to take effect.

5. The next time that the system is hung/frozen, hold down the RIGHT CTRL key and press the SCROLL LOCK key twice to cause the machine to bugcheck - if it's just Windows that's hung, the machine will bugcheck after you press this key combination. If it does *not* bugcheck and you've pressed the key combination correctly, you most likely have a hardware problem (base hardware interrupts like the PS/2 bus aren't being serviced, usually meaning the hardware's actually at fault, not Windows).