Thanks for the input guys. Attached is the vmware.log file. I decided to use the Debian 8 (Jessie) distribution and I am sort of able to get it working properly. When I open a file with gedit or if I try to utilize the search functionality in the filesystem, it crashes with the BSOD machine check exception still. There may be other interactions with the filesystem that could cause the crash as well but I am able to utilize the terminal, actions in the browser, and basic file attribute editing.
I can also verify I have not found a relevant thread that would point me towards the right direction besides the initial reply to this post about enabling Over clocking in BIOS configuration. I'm not entirely sure if that would work. I couldn't exactly find that option as simply as it is shown in the article that mentions about changing the clocking options.