You don't say what the failure is.  The exact error message would help.

I'm guessing you can receive mail OK from both accounts but have problems sending.

In general, you can only use the SMTP mail server of the ISP that you are connected via.
Presumably this is your Ameritech DSL.  That's do to ISP restrictions on spamming.  You
probably have problems sending via the university SMTP mail server.

There may be some workarounds depending on the exact error message that you get when
sending.

One common workaround is to use the SMTP server of your ISP in both accounts.