Running the Western Digital hard drive check on my hard drive while in safe mode found nothing. I am pretty much out of ideas. The computer seems stable now in safe mode, but only lasts about ten mins in regular mode.
On a side note, my motherboard beeps when I first start it up, as it counts the RAM. After it gets to 3328 MB, it pauses counting for a sec, and when it continues the beep stops. The beep isn't as loud as a POST beep, but it is coming from the motherboard. This started when I installed the new HDD.