Here's the screenshot.
This is the screenshot of how things looked for Total DNS after I changed the www CNAME to web.me.com.\
Would I have to do anything with the nameservers?
Something's not right with the DNS then. If it's parked at GoDaddy, then that is where DNS is sending you. This is a problem with your GoDaddy config, not Apple/MobileMe.
Do you have the CNAME set to web.me.com?
This is the screenshot of how things looked for Total DNS after I changed the www CNAME to web.me.com.\
Would I have to do anything with the nameservers?
