That test saying the hard drive is bad has nothing to do with the battery issue. But it does mean the drive is bad, even if it's working, a failed disk test means it has a much higher chance to fail. Make sure you have backups.
If you got a 3rd party Chinese battery off ebay or something, I'd try a different battery first. Aside from that, the issue may be with the motherboard or charger port on the laptop.