Well, I learned a lot.
Upgraded OpenFire...no luck.
Now, even worse, it was not logging anything to the error.log file.
BUT, there was a new error file called "nohup.out". The contents read "nohup: failed to run command `/opt/openfire/jre/bin/java': No such file or directory".
So, I went to that location. "java" was, in fact, there, so i tried to run it. I then got this error:
"-bash: ./java: /lib/ld-linux.so.2: bad ELF interpreter: No such file or directory"
Googled that error and discovered that glibc was needed. I installed it using "yum install glibc.i686", started the OpenFire service, and then logged in...
I wonder if this was a combination of issues that my journey resolved independently. I could probably research or think about it more, but I'm off to work.
Thanks for your help akherz!