MBP doesn't charge

I recently purchased a used MBP with Intel Dual Core processor, and so far everything is going relatively smoothly for being a new computer and OS that I'm not accustomed to. If some of you participated in my thread about downloading issues, I've upgraded to another internet service and everything is peachy now.

However, I'm having problems with charging my battery. I purchased this computer to take to class and general use, but when I unplug in the morning and close the clamshell to put it to sleep, the battery is completely drained before I need to use it in second class, which is about 1.5 hours from the time I leave the apartment. It displays that the computer has power when it's plugged in, but for some reason that battery doesn't charge. The green light doesn't come on the charger, although the display shows it's plugged in and working. The computer is perfectly fine while it's on charge, other than not charging.

I having searched around and couldn't find a solution to the problem, but then I inspected the magnetic plug to the charger, and it looks like one of the prongs on the end is set down further than the others, so I'm thinking that it's not getting a full connection needed to charge the battery, and that only enough to keep it alive is coming through. I lightly tapped the plug to loosen the prong, which I can then plug into the magnetic port, and with a bit g wiggling, the green light does come on, and it seems to charge the battery, but it takes quite an effort to get that to happen, and once I unplug I have to do it again. I may be fooling myself that this is the problem though.

It's a used computer, so I don't think it can be covered under any protection plans, or is my best option to spend $80 on a whole new charger? Has anybody else had this problem, or think it could be something else other than the charger's magnetic plug? I don't have any friends with Macs so I can't borrow one to see if it solves the problem.