Laptop batteries can be rather poor as well, so there could be an issue with your battery itself. Unfortunately, they usually go for about $60-80 depending on the brand/model. That said, a bad battery (that only works when it's plugged in on the charger) will wear out the HDD a lot faster. I've replaced a number of HDDs that were shot because their owners had poor batteries and thought a 35$ HDD was cheaper than a 75$ battery... well until I had to change the HDD again not even a year later. Replaced the battery AND HDD that time around and hasn't had an issue in the last 2 years.
If you want to take it to a shop they might be able to test the battery for you so you know for certain, but just keep in mind that a battery issue can really effect your system as a whole.