You can really get around that error directly, as SQL has control of master.

Back up the master db and restore it to a different name.

RESTORE DATABASE master_dbcc_checkdb

FROM DISK = 'x:\full\path\to\master.BAK'

Then run the check on that db. That should give you a very good idea of the extent of the errors you're facing.

Btw, make backup copies of all the SQL error logs immediately, before they scroll off and you lose the data. Only the log where the error first occurred usually has much detail on the error(s).