I'm not familiar with WalMart's branded browser but have you tried just setting up a new connection using the WalMart account settings (phone number, username and password) and then using it to try to connect?

If that connects okay, open Internet Explorer and try to access some sites. If that works, go to Internet Explorer's Tools>Internet Options>Connections tab, mark the connection you made as the default, check "Always dial my default connection" and IE should connect when you open it...bypassing WalMart's browser.

If it doesn't work, all you've lost is a little time.