You say that the iPhone is "constantly beeping" while this is happening. This leads me to think that this may have something to do with either the cable or the port on the phone. Apple's 30-pin cables have questionable quality sometimes, so it's very likely the wires have started to bent out of the contact, or that one of the pins (there's 30 of them in both the cable and the phone's port itself) is bent. These pins perform different functions, some are used only for charging, some transmit audio/video and are only used in docks, and some are used for data transfer and it might be one of those that's having problems.
What I would suggest you try now is try connecting your phone to another computer, even someone elses. If it still doesn't work, try using a different cable, again on multiple computers to verify your results. If the issue is still there then you may have to send your phone for servicing.
<Insert passage from "The Book Of Chrome" here>