Laptop Issue

Laptop problem, heres what it does.

When its plugged into the wall outlet you are able to turn it on but only for a matter of seconds. It would show the Gateway splash screen and the just shut off and try to turn back on and pretty much repeat this process over and over. Friend told me that sometimes it will stay on for a few minutes, and lately up to a half hour at the longest. However, when its not plugged in through the wall it wont even power on at all. I dont know much about laptops but it seems like a battery problem to me.

It's out of warranty and he told me he would sell it to me for 25 dollars lol. Basically I'm wondering if anyone has had any experience with this sort of problem and if it is the battery, are they easily replacable and or cheap?

I'm not sure if it stays on without the main battery installed i didnt toy with it much. I'm at school now but will try those when i get home and get back to you.