My Q works perfectly and always has. My Q is the grey Q from Alltel. Sounds like all you did was not check to see if it was really charging and now the battery is dead. I'd tell you to try to plug it into a USB at work there, but the Q won't start a charge via USB if the battery is that low.
You should also have the latest Motorola software if you only bought it 4 days ago. You can always check by installing Motorola's software updater and running it with your Q synced, but it requires a full charge on the battery to initiate.
Don't give up so easily. If the Q had such wide spread issues there wouldn't be so many of us loving our Qs
