There may a few solutions, these are based on my past experiences with the iPhone 4, so it might not work.
1. Just leave it for a few hours, then it should start working.
2. Restore it.
3. Just keep reseting
Also, since it recognized your iPhone when you plugged it in it most likely is not #1.
Other than that, maybe call tech. support or maybe use the Fast Track, as I think it's called, and then find the solution that way.
When trying to restore your iPhone in iTunes, you may see the following message followed by an error code 1601 or 1602:
The iPhone could not be restored. An unknown error occurred.
Or when trying to restore your iPod touch in iTunes, you may see the following message:
The iPod "[username]" could not be restored. An unknown error occurred (1602)
Completely remove iTunes and Apple Mobile Device support and then reinstall iTunes 7.5 or later. Click the appropriate link below for instructions on how to accomplish this for your operating system.