iPhone 3GS endless reboot after battery replacement fix
With a lot of iPhone 3GS units now requiring replacement batteries, but with no original batteries available, sometimes after a replacement when the power percentage drops to 30~50% the iPhone will turn off, but when you try to turn it back on again it goes in to an endless cycle of showing the Low-Battery screen and then attempting to start with the Apple logo, then restarting all over again in a minute or two.
The exact cause of the problem isn't known, though a mismatch between the presumed or old battery charge curve and the new battery is likely. Mostly the iOS installed thinks that the battery still has 30~50% of power left when in fact it empty, a lot of this is because lithium cells have an exceptionally flat discharge curve and thus estimating the energy left is not always practical without keeping track of the mAh consumed.
Put the iPhone 3GS into DFU/Recovery mode
Hold down the power button for 4 seconds
Hold down the home button for 10 seconds
Release the power button
Wait 15 seconds
Release the home button
Charge for 30 minutes
Exit from recovery mode
Press the home + power button for 15 seconds
Release both buttons
Press the home button for 3 seconds
The phone should now be booting into normal mode and you should be able to continue charging normally once more.