When I try running Mozilla (the stock one in Slackware, not Firefox) it doesn't open.. when I try opening in terminal I get:

bash-2.05b$ mozilla
*** Registering -webcal handler.
*** Registering text/calendar handler.
*** Registering webcal protocol handler.

And it just hangs. When I try opening it from root, however, it works fine. I tried chmoding /usr/bin/mozilla to 777 (which is probably a dumb and dangerous thing to do) and it still doesn't open with regular users. My question is.. why does it do this and how can I fix it?

Maybe try doing this: sudo chmod +x /usr/bin/mozilla, or if you don't have sudo, do su -c "chmod +x /usr/bin/mozilla"

If this doesn't work, mozilla's config file might be owned by root, or it was just a funky install.

Has it ever worked? If so: did you change anything? Install extensions, for example?
Who owns whatever directory mozilla is in?

Hmm, well.. after doing "ls -Rl / | grep mozilla-config" I get

-rwxr-xr-x 1 root bin 4104 2004-06-18 16:58 mozilla-config
-rw-r--r-- 1 root root 2309 2004-06-18 16:57 mozilla-config.h

So I think that means root owns it, correct?

Nope, it never worked (as a regular user). And root owns /usr/bin/mozilla for some reason.

Root owning mozilla shouldn't be a problem, as long as it's world (or at least group) executable. Also, your mozilla executes, otherwise it wouldn't be registering stuff.

Is /usr/bin/mozilla the actual executable or just a symlink? I'm asking because the default installation directory (as used by mozilla.org's own installers) is /usr/local/mozilla/ , though it may be different on Slack. On my system, /usr/bin/mozilla is just a symlink to /usr/local/mozilla/mozilla. All files in /usr/local/mozilla are owned by root and set to rwrr-xr-x.