Please help me with my resurrected A3!!!(multiple symptoms)

[Shaoran]

My A3 stopped working and the warranty had expired so I just threw it in my closet and forgot about it for months. Back then problem was that it wasn't getting pass the file scanning on the loading screen and it would turn off abruptly, also my PC wouldn't recognize it. The other day I got all sentimental about it and set it to charge with the ac adapter hoping a miracle would happen...and it did. First I noticed that when I connected the ac adapter the screen flashed white once and the the red light turned on and then it quickly went off. I left it there for a couple of hours and when I came back I started it and it did get pass the loading screen though it took like 15 mins. Now it works fine but I can't disconnect the ac adapter because it'll turn off.

Basically the symptoms now are:
1. Screen flashes white once when connecting it to the ac adapter.
2. It will not turn on if its not connected to the ac adapter.
3. Red light wont stay on.
4. PC recognizes A3 if the AC ad. is plugged in, but cannot get to the files.(I'm using a USB Host to load files into the A3.) If I USB it to my PC without the AC ad. the screen will start flashing white.

My theory is that the problem is a faulty battery but I'm not sure. So please!! can someone help me decipher this one so my A3 can be portable again?? Thanx!!!!!!!