Phone turns off after 30 seconds and needs to be Forced On

I just replaced the battery and now my iPhone 4s will turn off after 30 seconds of the screen being off. The only way to turn the phone back on is Force On (home button and power button).

History: Last week the phone would only turn on when plugged in and showed the plug into itunes logo. When I connected to itunes the only option presented was to Restore the phone, but when I tried I would get an Error (21) message. I found this could be fixed by replacing the battery, so I did that. I have since been able to Restore the iOS (8.3) and load a previous Back-up to get all my old data. However, now the phone will turn off after the screen is black for 30 seconds. The phone has not turned off when the screen is on and the screen can be turned on with both the home and power button if within the 30 seconds.

Please Help! I can not afford a new phone.