Thanks! I mainly use Chrome, and I've tried two profiles in Chrome, Firefox, Chrome on my phone, and two internet connections to see what it may be.
It must be related to my account. I finally decided to clear cache/cookies, which logged me out, and while I was logged out I could get to my cart just fine (and start the checkout process), but as soon as I log into my account, it just hangs and refuses to do anything. Guess I'll have to contact them and see if they have any suggestions.