Nexus 4 wont hold charge after screen and battery replacement
I suppose you prob got a new phone by now or fixed it. 

But if you say the "The new battery charged once successfully" you mean you were able to charge it only with the phone off?

If so, sounds like you might have had a short circuit somewhere near the battery's USB port connection, and only occurs when a certain circuit is on due to the phone being on. Or it could be just something is loose... hard to tell from the details given.

What I'd do is try and take it apart again and see if anything got damaged or loose around that area.

Gotta keep in mind these devices are very delicate and use low voltages. You gotta do fixes like this as if they were "surgery" and take all precautions, proper tools, etc. A bit of static electricity discharging from your hand or even damaging the track in the board somehow can cause big time damage. Tiny transistors are easily damaged by static electricity so always wear a anti-static wriststrap when doing these repairs.

Let us know what happened!?