Plugged In, But not holding a charge.

Okay, so my iPhone is plugged in, and it has a symbol on the battery, and the symbol is the plug, NOT the light bolt which indicates it's charging. So long story short, I want to know if my battery is damaged, like how could I tell?

I have a custom back on, and I think that's when I damaged it. Just to be safe, I have a new battery on the way.

OTHER INFO: The phone flashes off and on over and over again, it stays on about 2-5 minutes, and then flashes. It gives me time to do small things, like send a text, but even then it isn't really charging.

I would just like some help, I don't have a back up phone, and I can't afford to replace the whole phone from apple.

Is anyone else experiencing these problems as well? Just shed some light on this subject for me.

ALSO, I am going to leave it plugged in to see if over night it'll fix it's self. The battery looked kind of fried when I took it out, in the back it had a weird look, like an acid look to it. So maybe I discovered a problem early before it got worse.

Last but not least the side next to the dock connector, it looks like there's a dent there. Like a bad one, but at least the phone turns itself on. Did a clean restore twice so bare with me.