So the script installer provided by the hoster (which you pay for) did an upgrade skipping a version from 3.1 to 3.3 ... skipping 3.2. And, lemmie guess, helpdesk where you host said to come to community forums for resolution to the problem ... a script hoster provides you did the upgrade. No one in these forums works for hoster nor the company that makes the software that did the upgrade .... Hmmmmm ....
Anyhoo ... other than checking permissions/ownership, might try turning on Debugging (all the way to developer) and try to download something/anything. See if debug says anything.
You might also look at your apache (assuming you are running apache) error logs for things like 'warnings' related to downloads. Those warnings are not errors serious enough to halt something but might give a clue.
Right after the upgrade, did the site look 'wonky'? or was the site slower than before?
Go to Site Admin menu, Server, Environment and first update the component - link in upper right corner of that screen.
What, iF anything, does the environment check show that isn't 'green' or OK?
All hosters are not alike ... mind sharing with whom you host? And is it a cheapo package?
'spirit of sharing', Ken