The displays on my Motorola V6 Razr have gone blank and I can't make or receive calls. This started after a very light drop, flat on it's back

The case had become slightly warped. The lefthand side of the display hinge is also the main earth/ground contact for the display and this contact was no longer solid. There is a small gold plated contact that mates with the centre of the hinge pin.
Unfortunately, the phone body required a little bit of squeezing to make the contact good again. I used a quickgrip type builders clamp to apply just a small amount of pressure to the case. The phone is now fully functional.