iPhone isn't detecting new battery?

I recently replaced the screen on my iPhone with the help of ifixit. Everything went well except that I severed the cable on the battery. I quickly ordered a replacement battery and when I put it in the iPhone wouldn't power on or even show the indicator that it needs to be charged. I plugged the iPhone into a charger and the Apple logo appeared and the phone booted up normally. The lock screen said it was 100% charged so I figured everything was working. When I unplugged the charger the phone died instantly and will only boot when connected to a charger. It won't connect to a network or Wi-Fi just as if it had no battery plugged in at all. Is this a problem with the new battery?