Yes I know the Oracle Home and SID are set correctly, I checked those first. Here's what I got:

Code:
ORACLE_BASE="/u01/app/oracle"
ORACLE_HOME="/u01/app/oracle/product/11.2.0/db_1"
ORACLE_SID="BORG"
This system is Fedora 11.

When we've been trying to start sqlplus we've been using the following command:

Code:
sqlplus system@borg
I was unaware of the syntax you used for sqlplus (like I said I've VERY new to Oracle but learning fast) and I just tried it (logged into the server as user 'oracle' was the only way I could get it to work). And sure enough it brought up the SQL> prompt for me, no password required. Is that normal?

Anyways, I proceeded with your previous instructions:

Code:
SQL> show parameter local_listener
ORA-01034: ORACLE not available
Process ID: 0
Session ID: 0 Serial number: 0

SQL> alter system set LOCAL_LISTENER='LISTENER' scope=both;
alter system set LOCAL_LISTENER='LISTENER' scope=both
*
ERROR at line 1:
ORA-01034: ORACLE not available
Process ID: 0
Session ID: 0 Serial number: 0

SQL> show parameter service_names
ORA-01034: ORACLE not available
Process ID: 0
Session ID: 0 Serial number: 0
Okay so obviously apparently Oracle isn't even running?

Back at the command prompt:

Code:
[oracle@borg db1]$ lsnrctl status

LSNRCTL for Linux: Version 11.2.0.1.0 - Production on 21-OCT-2010 18:29:29

Copyright (c) 1991, 2009, Oracle.  All rights reserved.

Connecting to (DESCRIPTION=(ADDRESS=(PROTOCOL=TCP)(HOST=borg.ourdomain.com)(PORT=1521)))
STATUS of the LISTENER
------------------------
Alias                     LISTENER
Version                   TNSLSNR for Linux: Version 11.2.0.1.0 - Production
Start Date                20-OCT-2010 13:39:07
Uptime                    1 days 4 hr. 50 min. 22 sec
Trace Level               off
Security                  ON: Local OS Authentication
SNMP                      OFF
Listener Parameter File   /u01/app/oracle/product/11.2.0/db_1/network/admin/listener.ora
Listener Log File         /u01/app/oracle/diag/tnslsnr/borg/listener/alert/log.xml
Listening Endpoints Summary...
  (DESCRIPTION=(ADDRESS=(PROTOCOL=tcp)(HOST=borg.ourdomain.com)(PORT=1521)))
Services Summary...
Service "BORG" has 1 instance(s).
  Instance "BORG", status UNKNOWN, has 1 handler(s) for this service...
Service "borg.ourdomain.com" has 1 instance(s).
  Instance "borg", status READY, has 1 handler(s) for this service...
Service "borgXDB.ourdomain.com" has 1 instance(s).
  Instance "borg", status READY, has 1 handler(s) for this service...
The command completed successfully
I'm not sure why it shows 3 services in the bottom: BORG, borg.ourdomain.com and borgXDB.ourdomain.com.

Also:
Code:
[oracle@borg db_1]$ dbstart
Processing Database instance "borg": log file /u01/app/oracle/product/11.2.0/db_1/startup.log
It seems to start up fine without errors

Code:
[oracle@borg db_1]$ lsnrctl start

LSNRCTL for Linux: Version 11.2.0.1.0 - Production on 21-OCT-2010 18:31:31

Copyright (c) 1991, 2009, Oracle.  All rights reserved.

TNS-01106: Listener using listener name LISTENER has already been started
[oracle@borg db_1]$ lsnrctl stop

LSNRCTL for Linux: Version 11.2.0.1.0 - Production on 21-OCT-2010 18:31:36

Copyright (c) 1991, 2009, Oracle.  All rights reserved.

Connecting to (DESCRIPTION=(ADDRESS=(PROTOCOL=TCP)(HOST=borg.answeron.com)(PORT=1521)))
The command completed successfully
and then

Code:
[oracle@borg db_1]$ lsnrctl start

LSNRCTL for Linux: Version 11.2.0.1.0 - Production on 21-OCT-2010 18:31:49

Copyright (c) 1991, 2009, Oracle.  All rights reserved.

Starting /u01/app/oracle/product/11.2.0/db_1/bin/tnslsnr: please wait...

TNSLSNR for Linux: Version 11.2.0.1.0 - Production
System parameter file is /u01/app/oracle/product/11.2.0/db_1/network/admin/listener.ora
Log messages written to /u01/app/oracle/diag/tnslsnr/borg/listener/alert/log.xml
Listening on: (DESCRIPTION=(ADDRESS=(PROTOCOL=tcp)(HOST=borg.answeron.com)(PORT=1521)))

Connecting to (DESCRIPTION=(ADDRESS=(PROTOCOL=TCP)(HOST=borg.answeron.com)(PORT=1521)))
STATUS of the LISTENER
------------------------
Alias                     LISTENER
Version                   TNSLSNR for Linux: Version 11.2.0.1.0 - Production
Start Date                21-OCT-2010 18:31:49
Uptime                    0 days 0 hr. 0 min. 0 sec
Trace Level               off
Security                  ON: Local OS Authentication
SNMP                      OFF
Listener Parameter File   /u01/app/oracle/product/11.2.0/db_1/network/admin/listener.ora
Listener Log File         /u01/app/oracle/diag/tnslsnr/borg/listener/alert/log.xml
Listening Endpoints Summary...
  (DESCRIPTION=(ADDRESS=(PROTOCOL=tcp)(HOST=borg.answeron.com)(PORT=1521)))
Services Summary...
Service "BORG" has 1 instance(s).
  Instance "BORG", status UNKNOWN, has 1 handler(s) for this service...
The command completed successfully
I appreciate your help. Any insight is helpful. I'm sure it might just be some simple little thing that is the problem. The fact that the SQL prompt it telling me that Oracle isn't running yet dbstart is starting it successfully is kind of odd.

Also in /etc/oratab I have

Code:
# This file is used by ORACLE utilities.  It is created by root.sh
# and updated by the Database Configuration Assistant when creating
# a database.

# A colon, ':', is used as the field terminator.  A new line terminates
# the entry.  Lines beginning with a pound sign, '#', are comments.
#
# Entries are of the form:
#   $ORACLE_SID:$ORACLE_HOME::
#
# The first and second fields are the system identifier and home
# directory of the database respectively.  The third filed indicates
# to the dbstart utility that the database should , "Y", or should not,
# "N", be brought up at system boot time.
#
# Multiple entries with the same $ORACLE_SID are not allowed.
#
#
borg:/u01/app/oracle/product/11.2.0/db_1:Y
Which from what I read online this means that Oracle should start up when the machine boots up, so I'm not sure why it isn't.