Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
Rechargeable batteries fail after (usually, at an approximate minimum) a year or two of use.
Grease is not usually at all good for batteries, I'm surprised that you mention it.
The batteries fail either through inability to hold a charge, or through being unable to deliver sufficient voltage/power to power On the device.
Replacing rechargeable batteries usually can be done, yes. But JustAnswer.com is an advisory service (more or less) and does not stock parts. We can advise you where to purchase or obtain parts for repairs, and how to install them.
Let me know what other specific advise you need on this subject, please. Thanks.