My phone will not start up

The phone was working fine but sat for a long time, unused. I plugged it in and the lights on the front lit, so I let it sit and charge. Or so I thought. I got it to come on one time by removing and re-seating the battery and I though it was okay. Then I couldn't get it to turn on and I ordered a new battery since the original was several years old. Installed the new battery and the lights at the bottom of the screen lit up. After a reasonable amount of time, I tried to start up the phone. No luck at all. It appears completely dead.