CiviCRM failed to update to newer version

I have run into this problem on two of my websites that run Civicrm separately. Both are running version 4.5.8. When I run the automatic installer, the update process seems to freeze for an infinite amount of time and quits updating the database and all of the core files. With one of my sites, I was able to make a backup of the database prior to the error and reverted back to version 4.5.8, however, I wasnt able to make a backup of the other and now I am unable to update Civicrm at all, and it gives random errors when running certain tasks. I also am presented with the following error:

"Database check failed - the database looks to have been partially upgraded. You may want to reload the database with the backup and try the upgrade process again."

What can I do to fix my database so that I can be able to update CiviCRM in the future or is there a way to bypass the database check and have it update CiviCRM without further error?