Agree with smashogre that I would try another cable and another port. But realize your pc will probably not have the output of a wall charger and it will take longer. You're best off to use your Motorola supplied cable and wall adapter.
If your phone died because you let it discharge too low, it may be in protective mode which will also make this more difficult. I would put it on a wall charger for 1-2 hours then, with it still plugged in, press the power and volume down buttons at the same time for about 10 seconds. This should force it to reboot.
After that, do more frequent smaller charges to prolong the life of your battery. It doesn't need to be conditioned and has no memory so it will actually last longer and perform better if you top it off frequently.
Thank you everyone for your suggestions!
Lcb96744, I'm hoping you have been able to charge your phone by now, but I would like to provide some assistance. Once completely dead, many devices will only be able to charge by wall or car charger. I previously had an original Motorola Droid, and this acted in the same manner. In order to charge by the USB charger, the phone will need to have some amount of charge to it.
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Well they can do good things when your chips are down an need help. But i got to ask that inspiring Question were is your Original Charger. Bubba you need to charge it with it what came with the phone Ok if it has been lost there are Good place on Line. Like the Motorola Store, Android Central an Droid-Life to me android central is the best to go to an if they have the Motorola Charger in stock they can have it out to ya in a few days an they are not very expensive. I have seen them on there for as low as $14.99 an that is a Motorola O.E.M An most of these Guys on the post know how i am when it comes to Using & buying O.E.M Equiptment i am very animate about it. B33