You may want to open it again. Check if your new battery has the same APN- number as the original one (I got this wrong and my iPhone went crackers after a few weeks), carefully undo battery connector, clean with alcohol (IPA) or the like, reconnect and fix without touching with bare fingers, clean backside of battery connector as well, make sure the protruding spring connector for the back panel is bent up far enough to reliably touch the back panel contact spot (clean!), reinstall back panel. If it still doesn´t work with your new battery, try going back to the original one just to see if this was the cause. If it still does not work, you may have damaged the socket on the main board or unintentionally undone another connector.
Replaced the battery at the same time as a broken display, home button, and a fidgety dock connector. Got the battery from iFixit. Everything worked ok, though the iPhone seemed significantly more sluggish opening apps. After five weeks, a cold phone said " iPhone needs to cool down..." then began constant reboot every few minutes it had been up w/ Apple logo but not progress bar. Diagnostic info showed recurring kernel panics ("bug code 110") as reboot cause. Escalated through reboot, recovery, restores all the way to complete new and minimal installation. Cleaned and checked battery connector. No fix.
Last resort: swap back to the old battery - BINGO!
Finally found out that Apple uses more than one battery type for each iPhone model. Obviously, the iFixit battery did mechanically fit, but not logically. Ugh!!
And the lesson is: before replacing, open the iPhone, check APN-number on battery and order EXACTLY that one for replacement. Make sure you really get a new one. Lots of old junk on sale!