Been dealing with this for two days. Started with my 1st Incredible not charging above 70% ever, so I called Verizon and they shipped a replacement. The new phone charged to 95%, but then in the middle of reviewing which apps didn't backup/restore, the new phone started to drop charge, even though plugged in. Then this zero-charge problem began as well on the 1st Incredible. Both phones showed they were charging, but still dropped to zero and off.
Stopped off in a V store and the techs confirmed my charger is working, and the new phone is not. So V is sending a 3rd phone now, & I'm back to WM5 for a few days.
I could see where the USB port could become wiggly from the unplugging & replugging, but such a design flaw would be bad, esp considering the Incredible battery life issue & how often we're plugging them in. Instead I suppose it's possibly some software installed, but I've since wiped the new phone and it's still occurring. The old phone has never had such a drop-charge (or ultra-fast discharge) problem before the replacement showed up.
I wanted to send a few tips to try. Maybe they'll help someone else with this problem.
1) On a dead phone, leave the battery out for several-to-30 minutes, and then back in & see how high it charges. I only got as high as 8% on the new phone, but my old phone is still unresponsive.
2) Today's V rep suggested doing a hard reset, which completely wipes the phone. I did this once this morning, but rep said as high as the 4th times a charm. This is Menu > Settings > Privacy > Factory data reset.
3) Turn on Airplane Mode and install ATK Free (or your fav) to kill the extra apps and cut down battery usage while charging from near-zero.
But even with the above, these two still are not working. Lucky enough to happen right *after* I backed up to SD. If you're going to get a new phone, maybe try a friend's freshly charged battery to backup your apps/data while you wait.