This problem was due to the fact that the TEST table was missing.
After running the Project Verify, restored a backup of the project and ran this SQL to find that the TEST table was missing:
RPM_Restore = 313
default_rpm_db = 312
USE RPM_Restore --default_rpm_db
Run this SQL to restore the TEST table
SELECT * INTO default_rpm_db.dbo.TEST from RPM_Restore.dbo.TEST
The RPM project was restored from the nightly backup to a new database and the missing table(s) extracted and then imported in the existing database. The project was then Verified, Repaired and the Repositories Realigned. User is now able to access the project without error. ALM was also successful in launching an automated test remotely.