Bizzare power issue

Sorry if this is in the wrong section, or has been discussed before. I looked around for something of this nature, but couldn't find anything with as many different symptoms as I am seeing.

I have an aspire one D250 running xp that I bought used last March.
a couple of days ago, I noticed that the laptop was running on battery despite being plugged in. I unplugged it, and plugged it back in, and it started charging the battery. Since then, the problem has continued to get more frequent. It will sometimes happen when the laptop is sitting stationary on the table, and the power plug hasn't been bumped. Up till today, I would unplug it and plug it back in and charging would start again.
Today however, when I tried the same thing, it didn't start charging when I plugged it back in. I started playing with different stuff, trying it in the off position, battery out, ect. Here's what I found:
The computer can tell when it is plugged in, even if it isn't charging. When it is plugged in but running on battery, the battery light flashes and the power light turns orange. The battery status icon states that it is running off of battery. If the power is unhooked, the battery light turns off and the power light turns back to green. When the power is plugged back in, the computer reverts back to the previously mentioned state, although sometimes it will claim that it is charging for about 2 seconds before the battery light starts to flash and such. If you turn off the computer while it is in this state, the battery light goes to solid orange, and the power light remains solid orange. The battery does not however charge. At this point, if you disconnect and reconnect the power, most of the time, no lights come on. Every once in a while, when the power is reconnected, the battery light will come on like it should, and the battery will charge, just like it should.
Here is where it gets odd:
If I remove the battery and plug the computer in, when I hit the power button, the computer makes a low whine, which doesn't stop until I unplug it. If I then plug it back in and press the power button, the computer will power up just like it should, although it often shuts down very quickly, sometimes seconds after it powers up. Other times it will boot up and run just fine, and might run for hours before shutting off. If it does shut off, pressing the power button again will cause it to whine again, and the process repeats, with the computer starting every other time the button is pressed.
Other notes:
Wiggling the plug doesn't seem to make any difference in any of the previously mentioned symptoms, although the plug does feel disturbingly loose in the socket.
I checked voltage of the power plug with a multimeter, and it reads 19 volts, just like the tag on the power brick says it should.
Everything about the battery seems to work just fine. I'm running on battery power as I write this in fact. Hopefully I'll be able to get it to charge after I finish typing this, or I'll be checking for responses using my phone.