It does sounds like your batteries could be done for however that may not be the case. The batteries in my original HC are almost 9 years old or so but they still hold a charge for a lot longer than a couple of minutes but they do go flat much quicker than normal to the point that after a couple of months the HC won't turn on at all.
What I found a couple of times was that after charging (from completely flat in my case) I had to charge it again virtually immediately after it had said done charging; it didn't charge fully the first time. So you can try charging the HC, when done turn it on until the power bar drops the first bit then charge it again. It might work it might not but it's probably worth the try.
As for replacement batteries and changing them, there's threads about it here but any 1.2v NiMH rechargeable battery of at least 2400maH should be just fine.
If you end up changing the batteries, be aware the HC's don't actually turn off, they go into a standby mode so they are still consuming power. You should charge the HC every month or two when you aren't using it.
- Tim (no not that Tim)