My laptop, which has the .exe installed, prompted to restart to install a new update yesterday. I didn't do it yet because I haven't had one problem with Spotify on my laptop (and I didn't want to fool with it as I was leaving work). I'm sure it will auto update when I power up this morning. I'm going to download a new .exe and try reinstalling on my HTPC this evening. Hopefully they've fixed whatever problem is affecting random users and devices. And, for the record - I'm not a huge fan of the web player.
The problem seems to have gone away with the latest update. I did a clean install of the .exe and it's been working fine for 3 days now. It's just strange that the problem only affected ONE of my devices. Thanks for the input, peeps!