Hi,
Something funny struck me when looking at the BRCONNECT output: in your original post the command executed was'brconnect -u / -c -f check' launched from DB13, and this failed with ORA-01031. When asked later to post the output of a check report, you used the exact same command but from the command line and running as user sodadm, and this worked fine.
The difference between the two is that on Windows any command started from DB13 will run with the user 'SAPServiceSOD' whereas you ran it as 'sodadm'. The most likely explanation is therefore that, as Roman N advised, membership of the ORA_SOD_OPER group might be involved. Specifically, I suspect that SAPServiceSOD is not a member of the ORA_SOD_OPER group, while sodadm is. This is certainly the first thing to check.
If that doesn't help my second advice is to run BRCONNECT from inside SAP (txn SM69) with the parameters "-u / -c force -f check -TRC 3". This will trace all external calls and SQL statements and will reveal exactly for which SQL command the ORA-01031 occurs - the BRCONNECT log indicates it is the CONNECT / AS SYSOPER, but you want to make absolutely sure of that.
Regards,
Mark