BleepingComputer.com: Battery or Charger - Broken?

Hi all, my laptop has a problem. I don't know if my laptop battery is dead or the charger, or the charger port. My laptop battery is terrible. It used to die within 10 minutes or so with me using minimum stress on the RAM or processor e.g. lowest brightness etc. It would turn off unexpectedly too. It got to the point where I had to have it permanently plugged in during use. I was using it the other day and it was plugged in and it just stopped charging. It won't charge the battery at all now so I can't turn it on. Is there any way to test whether the battery is dead or my charger is broken?

Remove the battery, and plug just the charger in. Does it turn on then?

No it does not at all. I can hear the power pack buzzing. Does this mean it is the jack on the motherboard?

Does it usually buzz?

Well it is definitely making a noise when it is plugged in.

Look on eBay for a similar one. Could be its old enough, it's dying.

The power back or the battery? I'm not sure which its most likely to be, or the solders breaking on the motherboard from the heat of it being constantly plugged in for the jack parts.