Trying to diagnose what is currently wrong

Just replaced a bad battery, here's the phone's current behavior:

• No reaction from screen on power up
• Pressing the power button causes a single vibration
• Turning on a bluetooth headset that was paired to it and nothing else in it's life results in a 'connected' declaration.
  • Ran around and confirmed that nothing else had picked it up anyway
• Removing the charging cable and letting the phone sit for a while to drain resulted in it not vibrating when pressing the power button until I plugged it back into the charger.

I'm suspecting that I accidentally killed the screen when replacing the battery, but would like to hear if there were other checks I can perform or other possible theories.