1. press and hold the power and home buttons for 10 seconds to try a reboot of the phone.
2. Also try DFU mode - Connect your iPod via USB cable to PC. This should power the iPhone ON, then turn off the iPhone - press and hold Power + Home buttons for about 10 seconds, release the Power button while holding Home button for an extra 10 seconds. You’ll know when you’re in DFU mode, this is when the screen will go completely blank. If it does not go blank try again - it's all in the timing. iTunes should have a popup saying device detected in recovery mode or similar. Press restore. If prompted to restore from a backup (or similar) choose from the list your latest backup which should be just prior to the problem occurring.
3. download and install TinyUmbrella and see if your device is detected. If so select it in the connected device menu (may be shown as a 8dight number I think). If EXIT RECOVERY is not greyed out, press it OR if FIX RECOVERY is not greyed, press it. disconnect iPhone and try reboot as per (1.) above if it does not reboot by its self
4. Check the dock connector - perhaps it has been damaged somehow.
5. What happens if you plug it into a wall charger?
6. Have you tried a different cable to PC?