CSS and stuff for themes are found in moodledata/localcache/ in 3.1 Since the site is having rendering issues could be that what was cached when site was lower version didn't get -re-cached. I just did a search of plugins and you are correct ... snap shows compat for 3.0 but not for 3.1 ... thus maybe you were upgrading from 3.0.x to 3.1.x and that's why the upgrade failed.
Anyhooo ... if one moves the 'snap' (assume that's it's name) out of moodlecode/theme/ and moodle cannot find the theme it's supposed to use, it should default to one of the core themes that come with 3.1 (canvas, more, or clean I think).
In version 3 now it appears there is deeper ('better'?) checking of compat plugins.
You might need to turn on debugging. If you can't get to the UI to turn it on, there are some lines in config-dist.php that you could copy into config.php to turn it on.
What debug kicks out will (hopefully) tell us what's going on.
'spirit of sharing', Ken