Hi everyone.
I had the same problem on an iPhone 4s, running iOS 6.0.1 and solved it this way:
1. I did a hard reset, as follows:
a. turn on your Mac/PC
b. plug in the connector cable into your Mac / PC; but do not connect it to your iPhone yet.
c. on your iPhone, hold the power button (top right corner) and the home button (the round one at the bottom) together for 10 seconds.
2. When the phone goes black, release both buttons and very quickly plug the connector cable into the phone and then immediately hold down the Home button again. (when I was too slow connecting the cable, I found the Apple logo would reappear and I would have to start the process again)
3. Now, when the Apple logo appears keep holding the Home button. Soon the screen will change to the "Connect your phone to iTunes" image.
4. You can now release the Home Button (also, iTunes will most likely start up and tell you that your phone is in recovery mode. Do not restore, as you will lose your data.)
5. Now, carry out another hard reset - so follow step 1 (a and b) above.
6. This time, as it reboots, leave it to reboot and with any luck you will see the usual iPhone unlock screen. Make sure you unlock your phone ASAP. I missed doing this the first time and as soon as my iPhone screen went dark I had to restart the whole process again.
(Please note, that this whole thing happened to another friend of mine; but in stage 5 he simply powered the phone off, rather than hard rebooting and it still worked. Worth trying if it's not working)
7. Now your iPhone is unlocked and it should automatically appear in iTunes - now immediately BACK UP YOUR PHONE!
I hadn't backed my phone for a month and had hundreds of photos that I would have wept if I had lost. But thankfully the phone is back up and running and I now have a back up at least.
If this still doesn't work for you, try variations; such as disconnecting your phone before the second hard reset. All I can say is that is has worked for me and another person, so I hope this helps someone else get their iPhone working without resorting to the dreaded "restore and lose all data" option.