ORA-01722 indicates some code is hurling an INVALID_NUMBER exception.
Connect as a DBA and have a look in DBA_TRIGGERS. Is there an AFTER LOGON trigger? If so, look at the code in the trigger body. Is there anything which is doing a TO_NUMBER() conversion; remember to consider implicit conversion (inserting a non-numeric value into a numeric column, etc).
Regular users are stymied by errors in LOGON triggers but DBAs get a free pass. Otherwise, who would be able to connect to the database and fix the problem?