ASUS model Q553U doesn't work

History: Last night I went to our local recycle center to recycle waste paper, cans, bottles, metal items, etc. I noticed a laptop computer box propped up against the bin for cardboard. I picked the box up with plans to toss the box into the cardboard bin. To my surprise the box had an Asus computer in it. I took the laptop home to check it out. I assumed it would not work and I was right. Here's the odd thing. That computer looks like it just came from the store. It absolutely does not look used. There are no scratches or smudges or dirt/dust on the keyboard. It's as clean and nice as one would expect a newly purchased computer to be. According to a sticker on the box, the computer was purchased as an open box purchase from Best Buy.

I plugged the computer in using the AC adapter. After about a minute I could hear the fan running. The Capital Lock key had a light. The screen stayed black. The DVD player would open. The computer will not power up without being plugged into the AC adapter (dead battery?).

Considering the laptop looks like it has never been used I thought it might be worthwhile asking about fixing it. I'm thinking the battery might be dead for one thing but there must be other things wrong also. Any thoughts?