Chosen Solution
Iphone 4s constantly turns on and off, home screen comes on then goes to apple logo and back to home screen. Also battery does not seem to charge
I’d try changing the charging port and battery, if that doesn’t help it could be a board issue, has the phone ever been water damage?
My guess is that you have damaged the solder connection of the battery connector socket to the board while changing the battery. Take a close look at the four solder pads to see. The connector can be replaced, but probably best for a professional. Jessa
Not charging doesn’t mean that the phone is broken, so don’t give up! I had this issue too, and it turned out that the only problem was that a screw wasn’t tightened all the way which was preventing the battery connector from fitting properly.