Should it fail consistently with any computer, and with any cable, take it to one of your mobile provider’s stores and let them deal with it. Considering what you’re paying them every month, they really should fix it.
But if you see the USB icon, then the phone just may be set to use the connection in a way other than the one you want. Pull down the top bar on your phone and select USB connection. There you’ll find several ways that the phone can connect to the PC. Pick the one you want.
One hint: If Windows Media Sync doesn’t work for syncing media, try USB Mass Storage.