Rick,
have you tried to telnet to port 3306 of the machine where the mysql server is located, from your home machine? if so, what do you get? If you're successful you'll get a connect bit that includes a string that will show your mysql server version number. if you don't have mysql access you'll likely see a mysqld reject of some nature. if there's a network issue you'll just get a hang or you could get an unreachable error.
Yup, it works:
$ telnet 173.13.167.209 3306 Trying 173.13.167.209... Connected to mail.mailnewsrss.com. Escape character is '^]'.
4 5.0.77aWqQ!OMq,slG]|xft5L[fConnection closed by foreign host.