What I don't get is that it works on your home Wi-Fi. I could see it only working on campus if the SMTP server required authentication if you're outside of the campus network. I don't see why it would work on your home Wi-Fi and not on EDGE.
Conversely, you could use cwmx.com with no authentication and it would work fine on EDGE, but would not work on Wi-Fi.
You could try using your home ISP e-mail account's SMTP server, but then your e-mail would be, just like on cwmx.com, rejected by any domains that do RDNS lookups. While this is a dated and ridiculous practice, some IT Admins still do it because they don't know how to filter SPAM effectively.