Help with unusable iphone 3g.

[i'm.huMAC]

I've been having trouble with my iPhone 3G.
It can't be turned on unless it's plugged to a wall charger. When it turns on, it shows me the Apple logo for like a minute then the "Connect to iTunes" screen. Whenever I unplug it from the wall to plug to my laptop, it dies.
It won't turn on when I plug it to my MacBook. I was hoping restoring the device would fix the problem but how am I supposed to restore if it won't turn on when plugged to my laptop?

 

[PsstGreek]

How long are you letting it charge for? It could be the battery going bad.

 

[i'm.huMAC]

Yeah, I guess my battery's gone bad already. What could I do about it?

 

[sou1 so1di3r]

Replace the battery with a new one. You can get them off ebay fairly cheap I believe