Hi
From the details of the issue pasted above -
LOG BY0=> ORA-01033: ORACLE initialization or shutdown in progress
looks like the DB is not okay when you are observing the above.
First check if the DB is open and running - select instance_name , status from v$instance;
Also check the alert log for any issues -
If it is OPEN , then check if listener is running and if it is listening to the service for your SID.
lsnrctl status
if both above are okay - then check R3trans -d . This needs to be working fine.
If yes , then ensure that all SAP Processes are clean and then do a fresh start of SAP . Run cleanipc before starting up SAP.
Also from your initial post - LOG GZZ=> 1 possible network problems detected
Please check if DNS hostnames are getting resolved fine at the OS level .. as sometimes the SAP connection to the DB fails due to network issues.
Thanks
Rishi