Alright, it appears I've fixed the problem. Like I said, it was a software issue.
I uninstalled IDT Audio High Definition from Device Manager (and checked the box that gave me the option of removing the drivers forever) and restarted the computer. Windows automatically installed a generic sound driver, and everything seems to work fine now. An added bonus is that I also don't have that worthless Beats Audio software anymore.
I just hope IDT doesn't try to reinstall itself again. The first time I uninstalled it (about 2 weeks ago) Windows just gave it back to me. For those of you have the same problem I had just be persistent in uninstalling IDT until Windows gives you the Generic Driver.