Same problem:
I installed IOS7 on my iPhone 4S as soon as it was available.
It first worked ok for a couple of days.
Then yesterday after loading battery overnight, the battery was only at 48%, a few minutes later it went to zero.
When connected to a wall charger it was showing 100% battery load, but disconecting it was shutting down for low battery.
I tried to restore in DFU mode but I got the error 2001 after waiting a few second for the iphone to answer, which was not happening due to low battery.
I replaced the battery, with one that was at 50%. Then I could restore it, and it seemed to work normally.
Then after a few hours on without use, it appears to have switched off for low battery again.
I tried to load the batterry over night, but it was just keeping in a continuous rebooting loop, and not charging.
Trying to restore from iMac or Macbook gives 2001 error.
So it was not the battery, it is just not charging the battery on any computer or wall charger.
It's dead.
What can I do, please help me !!!!