By rebuilding the master, you can set the appropriate permissions to allow you to attach the databases. Unfortunately you will also need to recreate anything else stored in the master. Logins (both NT and SQL) would need to be recreated, and sometimes there are issues with recreating SQL Logins.

Since it sounds like you are locked out, however, not sure what choice you have. You could transfer the files to a server to which you have access and reattach them there, but if the logins aren't correct, you may lose some permissions.

For the future, remember that backing up and testing the master restore should be treated as important as the most mission-critical database on the server. It's an odd restore, so it needs to be practiced from time to time.