After I got home with my stolen iPhone I found I couldn't reset it. iTunes told me I had to enter the passcode. What could I do?
Cough. Ok, seriously. For the 2nd time our good friend C. has given one of our kids her ex-iPhone . C. is a wonderful person, but she has been heck on iPhones. This one has a broken screen, I'll attempt a FixIt repair after I've tested the phone. I didn't want to bug C. for her passcode (after all, it could be her bank PIN too), but Apple documents a procedure for initiating recovery mode on a device that won't mount in iTunes: iPhone and iPod touch: Unable to update or restore.
Be sure to hold the home button as you connect the cable. If you do it correctly the recover dialog appears quickly.
 When both her brothers had iPhones, it was clear my daughter's wrath was building. That is not something any sane human would choose to face. Getting this one for free was a lifesaver.