I had the same problem. I spend 40 minutes with tech support who were quite helpful but eventually agreed phone was faulty. I have sent it back and am awaiting replacement. (purchased directly from Nokia)
theres a task running in the background which is invisible to end user and tries to connect . install mobishield antivirus and kill the tasks running, disable autostart . then all will be fine . elsewhere do a soft reset
If widgets have been ruled out, other common things that could be connecting to the internet are e-mail, Mail for Exchange, and perhaps A-GPS and network-based positioning if you use Ovi Maps or geo-tagging in the camera.