Hi M,
RH 6.1 is a really old release of Linux. I recommend not going through the tedium of browsing through those advisories which are really cool for the techies but could perhaps take away a lot of your precious time. A better bet wouldbe to do a fresh install of RH 7.2 (latest kernel/binaries) from a retail copy of Redhat media. There have been too many vulnerabilities since the RH 6.1 release.
Since you say, you have a feeling that nothing is patched, it would be in your best interest not to engage in reading advisories or browsing bugtraq, but proactively install the latest OS builds available. Ofcourse this will call for upgrading all applications presently configured for RH 6.1 to RH 7.2.
I wonder, how you have been able to survive the attacker attempts. Or may be you weren't online at all ;-)
I think guys at NSA/NIST and a couple of other guys are working on creating documents related to building secure RH linux installations. However linuxdocs.org has good great guides and HOWTOs on to build and configure secure RH linux systems and sites. Let me know, if you need more help on this.
Thanks,
--Rookie