iPad Screen Light Up But Won't Turn On

My first generation iPad has had a problem where I plug it in, and the screen lights up (just gray, no Apple logo or battery symbol) but it won't turn on. It'll turn on and off every 15-20 seconds or so.

I have tried holding the lock button and home button together as well as loading it into recovery mode via iTunes and it will not respond at all.

What could be the problem here? The only things I can think of are that the LCD is damaged, the battery pack is bad, or the logic board is fried. Before I replace anything though I wanted to ask if anyone had any input.