Different Cords are they by chance Motorola OEM's or something of the Other it's best if you can to use the Cord that came with the phone.. )
Have you taken say like a Flashlight and Looked at the charging port you may have some Fuzz or something like that obstructing were contact need to be made if there is some in the port you can do these three different things
Give these Suggestions a Look at if there is stuff in the Port Removing it should bring the Charging Back but if Doesn't then I would Visit the Local Corp. Store in your Area and have them using one of there chargers check the phone if it determined that there is an issue you can either have them Get you a Certified Good as New one or Send your Razr to Motorola for Repair of the Port..
I know the frustration of not having the ability to charge your phone properly robbob67 because I've been in that position. B33 gave some awesome steps and suggestions for resolving your issues. I would like to add if your phone can not charge and you have checked it over for damage, a store evaluation might also help locate any problems you may have missed. If the phone is still under warranty and no damage, we can replace it with a certified like new phone of the same model. If there is damage or the phone is out of warranty, you will need to review other options, for instance insurance or upgrade if you're eligible. Please keep us posted.