You can use any email program with any Internet connection.
Make sure your Windows Mail is not specifying a specific connection.
In Windows Mail go to Tools, Accounts, select your mail account,
Properties, Connection. What does it show for connection?
You must either leave that unselected (in which case WM will use whatever
connection IE uses), or else select the Local Area Network.
Also, under Tools, Options, Connection, the first box should be checked,
and the second box unchecked.
If all that checks out, but you still have the problem, the account may be corrupted.
Delete the account, restart Windows Mail, then recreate the account.
We don't provide support for Incredimail here.