With most phones, if your battery gets too low, you take the battery out and place it on an external charger and when it is charged, put it back in the phone. Since the Razr and MAXX have permanently installed batteries, this is not an option.
Now, your phone goes by what it "thinks" is full and normal and counts down in between. If your phone is not calibrated, it might think the phone is at 10% (when the warning to plug your phone in pops up)when it is far less than that. So you think you have a few minutes to wrap up your text or game or whatever when you really do not. Then the battery gets so low that it will not charge as Tis described above. The one thing that might work will be to leave it on your original charging cord and charge it for a long time. Try it. Next is get a factory cable. Here is a link that talks about them.
http://www.droidforums.net/forum/sm...-style-programming-cable-droid-razr-help.html
Of course, you can send the phone back and get a replacement.
However you do it, once you get your phone operating again, you need to calibrate your battery so your phone "knows" (vice thinks) where full and empty are. It is very simple and Foxkat has devoted several threads discussing this and has dug into the why and not just the how.
this is his system aka "Foxkatting" you phone!! :biggrin: Use you phone until the actual screen pops up and tells you to plug the phone in. This is at 10% for ICS (15% if you are on GB and have not updated to Ice Cream Sandwich). Then charge your phone overnight to ensure you get a full charge. The next day repeat the process. This will teach your phone where the limits are. You will be good to go for about 2-3 months. Repeat the process.
There is also a good discussion on why it doesn't matter whether you run your phone to 10% and recharge or recharge at 50 or 60%. If I find the thread, I will update this post with a link.
Good luck! ilovedf