Nope that would not tell me anything. The DB Table Prefix Change code changes all DB Table Prefixes and simultaneously changes the wp-config.php DB table prefix variable. So if the DB table prefix variable is not successfully changed in the wp-config.php file then this will create a database connection error and or a redirect loop until the variable is changed in the wp-config.php file. In testing the solution was just to manually edit the wp-config.php table prefix variable and the this solved this particular problem. Unfortunately, we do not have a DSO testing server available at this time. it was dismantled/wiped out quite a while back. Logically the worst case scenario is: all DB table prefixes are changed, but the wp-config.php table prefix variable is not changed due to a problem with the wp-config.php file (DSO, or other problem) and the solution is just to change the variable manually. In your case, I would suggest that you do not use the DB Table Prefix Changer tool on your sites since there may be some other factor involved since the normal scenario did not occur and something we did not encounter during testing has occurred on your particular server.
Logically if your wp-config.php file is writable then you would be able to use the DB Table Prefix Changer tool without any problems. Create a test WordPress site, make the wp-config.php file writable and then run the DB Table Prefix Changer tool on that test site.