It sounds like the theme is hanging when you try to disable it.
Physically remove the theme. Login over FTP and delete or rename the theme directory. If that doesn’t work this will take a lot of debugging. WordPress will notice that the active theme is gone/broken and load a default theme.
I tell you the following with great caution. Try this only if no other options are available, and just before you cash out and reinstall.
You can also try manually switching themes. Search the $wpdb->options table for current_theme in the option_name column and change the associated option_value to “Twenty Thirteen” (I am assuming that theme is on your system”). Do the same with the template and stylesheet values but change them to “twentythirteen”. Edit carefully. You can break things. That will force a theme switch, or it does when I try.
As with any database edit, back things up thoroughly first. This has been tested but not thoroughly. Do not ignore the “back things up” part. If you don’t know how to back up the database (not the PHP files), then stop.
I don’t know what else your theme might have done, so no guarantees. The fact that renaming the directory did not help gives me pause. There will still be entries in the database that should probably be cleaned up.