The issue described here is mostly caused by the battery becoming so low that the device won't charge it anymore. It doesn't matter how long you leave it connected for.
The solution is to charge the battery externally, with special equipment, which doesn't help many.
You can send it to a number of people, including myself (I'm I'm Australia though), and they can do this for you. Alternatively you can have the battery replaced, but if it drops below 0% the same can happen.
Best bet is not to leave the phone sitting in a flat state at any point.. Also, try charging the device from the computer as sometimes this will tell the device to charge the below 0% battery.
For the guy who mentioned FTM, that's a firmware upload mode. Either one of the volume buttons are stuck, or the device has corrupt firmware, which is normally associated with going flat during an update or something like that. It's a seperate issue.
For informations sake this effects many phones on the market.