I've now owned several Droids, and so has my wife (long story, for another time). We have had the charging problems in spades.
In my experience you can't expect the Verizon service people to have even a reasonable understanding of the problem. They will just send you another phone if they determine the one you have is clearly not working. They're not stupid, they are just not trained and no one bothered to give them a correct script to work from. Although it would save the company a fortune in returns.
OK, flame off, back to the problem.
What I have learned is that the Motorola Droids (and maybe others, but all I've owned are Motorola) need a lot of current when they are charging, and even more so when they are almost discharged. I have a reasonably new computer, but when my Droid is really low on power it won't charge from this computer. So I hook it up to a beefy wall charger and off it goes.
For car chargers, I find that the iGo chargers from Radio Shack are pretty good and will charge the Droid pretty much any time. Other car chargers may or may not. And, by the way, my computer will charge the Droid just fine when it's above about 50%. You can see how that would throw one off--hey, it charged on the computer yesterday--but that's how it goes.
My advice? First, try the wall charger that came with the phone. It likely has enough oomph to charge the phone even when it's quite dead. Or, if you've thrown it away as I have, get a new charger with current capacity approaching .5 amperes. As I said, iGo from Radio Shack is good, but so are lots of others. I'm now charging mine--that just now refused to charge at the computer--from a Kensington wall charger that has 4 USB sockets. It's nice to have all the sockets, but use care when charging lots of phones if some of them are very low, since the result may be that not everyone gets charged.
Good luck! I think the Droid phones are great. I wish Verizon understood the importance of customer service--it would save them a lot of money in returns that wouldn't have to be made, and you and I would not have to solve these problems by ourselves using trial and error.
try another usb port but usb is a poor way to charge the batt.
if you look under menu/settings/batt, at the bottom it says you won't show a full charge with usb charging.
i have the phone off & charge with wall adapter for 3 hours.