Charging Laptop Troubles -- What Part to Replace?

My name is Devin Fitzpatrick, and I'm a freshman in college, and don't know that much about computers, especially not hardware -- but the resident computer consultants told me this forum is really helpful so I'm hoping you guys can give me a little advice. I'm afraid I don't actually have a Dell Inspiron -- I have a Latitutde laptop, an older make -- but since this isn't really a software problem, I don't think it should matter that much, and I didn't know what other forum I should go to. I hope this is okay. It shouldn't be too much trouble; I know something's busted beyond repair, but I just need to find out which part to replace, and see if anyone else has ever suffered the same problem. Because it's pretty crazy.

At some random point yesterday, my laptop started running out of battery. This began to seem pretty strange once I realized it was still plugged into the wall -- then I realized that the light was off on the AC adapter (that black box on the power cord, in case I have the term wrong), so I tried different sockets, and none worked, even ones that had been working on desk laps and radios. So I assumed my power cord had just burned out, and took it into a shop. But when the guy plugged it in, it lit up fine. And then he plugged it into a laptop that the cord would fit into, and THAT worked fine. So I was like "Huh!" And went back to my dorm, feeling silly.

Only it didn't work when I got back. Then, having a creative idea, I tried plugged the power cord into the wall and NOT plugging it into the laptop. The green light turned on. And then I plugged it into the laptop -- and the AC adapter light went OFF. And then I removed the power cord -- and the light STAYED off. Even though it was still plugged into the wall.

Yeah...

When I remove the plug from the wall and plug it back in again, the light turns on again, of course, but every time I plug it into the laptop the AC adapter light turns off. It's the weirdest thing I've ever seen. The only possible logical explanation seems to be that it's my laptop's power input thingie that's burned out, and it's so freaking burned out that it actually reverses the eletrical current or something and makes it so the AC adapter is cancelled out completely, and thus the green light stays off even after I remove the cord from my laptop, and I'm forced to unplug it from the wall and replug it to turn the light back on again.

So my question is: what part on my laptop, specifically, is burned out? I can handle being without my laptop for the time it'll take for a part to ship, but I think if I order the wrong part and mess up things will start to get bad for me, what with having to write essays and stuff. So if you wonderful people at the Dell forum can help me with some hardware knowledge and tell me what part specifically should be the one that's randomly died on me, I'd really, really appreciate it.

Hope you all had a good Labor Day weekend! Peace!