I've got the same behavior. Fresh install on a Debian 8 server, Sonarr 188.8.131.5253 & Mono 184.108.40.206. Worked fine for a few days, UI was non responsive this morning (possibly my fault, I had a non responsive mount and ls & df were both hanging). I fixed the mount, Sonarr was still nonresponsive. Restarted it, and now my logs stop at Starting Web Server like yours, and nothing responds.
I followed the advice in this thread - installing mono-devel and mono-addins-utils and rebooted, and my log did progress to the next steps, looking for releases.. But the web UI still timed out, and the next restart halted at starting web server again.
Attempted to update to Mono 5, installed mono-complete -- no change.