How to fix the PDOException shown after upgrading to Drupal 7
If you manually edited the schema_version column, you practically avoided Drupal would execute the necessary updates, and add the necessary fields in the database tables. That is why you get that error message.
How many updates you blocked depends on the number you set for schema_version; if you set it (for example) to 8000, then you avoided Drupal would execute all the updates.

To fix it, you can only restore the values schema_version had and run again update.php. This is not 100% error free: In some cases, executing the same update twice could cause an error that would stop the update process. It would be much better if you would restore the database from a backup you have from before manually editing the system table; in that way, you would be sure that executing update.php would not cause any runtime exception that would interrupt the update process.
The only alternative I see is executing the updates that were not executed, but you should have to track which updates were not executed or were executed but stopped because some error. It is also difficult because some updates need to be executed in a specific order; see system_update_dependencies() that defines the order for some of the updates for the System module, or node_update_dependencies() that does the same for the Node module. In short, you should write code similar to the one used by Drupal to update modules, adapting it to your case.