Then at some point, you downloaded the new moodle code. Or you used some installer that automatically upgraded your code. If the latter, we cannot help - you need to talk to your host about their installer.
For now, if you installed manually, it sounds like you have three options:
1. Hope that the installer did not actually get started and remove the 3.5 and return to 3.4 code, copying over your config.php file and see if that gets the site back online.
2. Restore a backup from before you started the upgrade.
3. Wipe out the database and start from scratch.