Do you have anything like a firewall or IP blocker running - it could interfere with registering - could be worth a quick disbale and test (and then re-enable afterwards)
ff/ie should have nothing to do with the registration. runs it's own program. i'd just disable the firewall, or check & see if MS/AV/etc. is blocking it.
I too run Firefox and I actually had to open it during registration to "show" Vegas that it was connected to the internet. Then the registration went through in a blink.