Issuing sqlplus that way gets you in as SYS using OS authentication instead of database authentication. SYS is kinda like root -- not a good idea to use most of the time, but there if you need it. You can set other users up for OS auth if you ever wanted to.

I have a suspicion you are running into case sensitivity issues. Some of the config files you listed don't care, some do. Can you type this and see if 'borg' is in there as a running database? I think you will see that 'borg' is up and running but 'BORG' is not. Also you can set $ORACLE_SID to borg and then try sqlplus again (both ways). You can try some of the parameters that failed before to see if it is running.

ps -ef | grep pmon