Yes - Using the Wi-Fi It doesn't make sense that if I connect up to other modem it works fine. But as soon as I change the SMTP to the new one everything goes bad.
Maybe your wireless connection makes you use the wifi providers smtp server. Out here ATT on DSL forces users to use ATT's SMTP server and blocks outgoing port 25 traffic otherwise, and their SMTP configuration requires using a different SMTP port in your email client.
Your best bet is to verify the necessary configuration with your provider.