I'd say reset the device once more while its plugged in and leave it be for roughly 15mins.
For the iTunes part
- Make sure your up to date with iTunes
- Make sure your cord is plugged into the computer directly (tower or side(if laptop))
- Try resetting the AMDS (http://support.apple.com/kb/TS1567)
If issue persist for both parts then you might need to place device in recovery mode (http://support.apple.com/kb/ht4097) and restore device as new. Hope it doesnt reach that point.
hope this helps a bit.