If you entire computer is crashing, it is likely not a problem with After Effects, but a problem with hardware---such as bad RAM, and inadequate power supply, bad drivers...
Do you encounter the same problems when you try to use, say, Premiere Pro or Photoshop?
Thanks for the quick response. I was figuring that may be it, so I am in the process of downloading the program on another computer and trying to render from there. I'll let you know how it goes. I haven't had those problems using any other Adobe software that I use including Premier and Photoshop.
Without seeing the crash logs, none of your info matters. If it drags down the system, it is indeed more likely a driver issue or something similar.
Well everything worked on my other computer, though slower. Since it seems to be the hardware causing the issues, could someone point me in the right direction as to which component is causing it? My log file is at the link below:
Thanks for the quick responses and help!