Try purging all caches in Settings > Site Admminsitration > Development > Purge all caches
Then after that has completed refresh your browser. And logout. And close browser.
Next open browser window. Login and try to complete the file upload. If the same problem happens again, try anothet file. Just make up a simple text file and see if that uploades. If not then there may be a bug in the system. In which case you may consider upgrading to Moodle 2.0.8.
Normally I would suggest you report this as a bug, or check to see if it is a bug, but since Moodle 2.0.x is not being updated now only for security issues, I don't see you getting anywhere with the problem without upgrading first.
You will find Moodle 2.1 much better.