There are several possibilities here:
#The flex connecting the battery to the logic board may have been damaged, rendering the battery inoperable even if the cells are holding a charge. If you have a multimeter, measure the voltage, it should read ~3.7V to 4.2V depending on the charge state.
- Where did you buy your replacement screen from and how much did it cost? There are many poor quality screens on the market and you typically get what you paid for. It is possible that your replacement screen is defective.
- If you connect your phone to an iTunes enabled computer, does iTunes recognize your phone? If it does, this could indicate a defective screen or damaged LCD or backlight circuit.
- Did you unplug the battery before changing the screen? This is a best practice to avoid damaging the backlight circuit on the logic board.
If you haven't already done so, follow these guides when disassembling your phone.