I installed the Slack 12 imapd/ipop3d package, added them to inetd.conf (yeah, yeah, I know, but that's how both the daemons are written to work), and restarted inetd.

Now, when I try to use my mail client (KMail) to download my email from the server I installed them on via POP3, it disconnects immediately.

This is what I got from an attempt at talking with it manually:

kmw@rerun:~$ telnet charliebrown.outwardhosting.com 110
Trying 66.160.141.192...
Connected to charliebrown.outwardhosting.com.
Escape character is '^]'.
Connection closed by foreign host.

It just disconnects--no message is given (as required by the RFC), nothing at all.

Any ideas?

Could be tcpwrappers... check /etc/hosts.allow & /etc/hosts.deny

Both are empty, which according to hosts_access(5) means every request should fall through to "access is granted".

That's correct.

No clues in the maillog?

Nothing relevant to ipop3d...just the standard notifications from sendmail that it's doing its job.