First, check if you got zune up and running on the pc when connecting the phone.
Originally Posted by onemorechanc
Most WP's have a locked bootloader, so it won't be detected as a mass storage device.
Only when you fire up zune your phone will get detected and connect.
Only way to overcome that is to flash your phone with a FW that has the unlocked Qualcomm bootloader.
If it doesn't connect with zune started up, then you should look for other causes:
Most likely it's just a driver problem on your pc. Check if other devices work on that usb port, and also do the reverse and check if your phone connects through other usb ports and maybe on other pc's.
You can use logic deduction from there : if other devices don't work on the same usb port, it'll be a driver issue for sure. If others do work, try to connect on other ports or pc's. If it don't work then either, it'll probably be the cable or your phone. And so on...
you'll end up with finding the cause.
EDIT: just saw "internet connection"...so the above could be useless to you :p
I just use my home wifi to connect to my home network. I don't think you can actually use ICS with a phone.