Depending on what brand they are, see if you can get the management app for them. Many brands have it, some don’t. This will do a few things like tell you if the drives have the latest firmware on them, and also total TB written and a “health” status. If the drives report a ton of TB written they could be close to end of life.
You can’t just “unplug the battery” though as they are suggesting. Any modern laptop requires you to open the laptop up by removing the bottom panel to gain access to the battery.
A repair shop should at least be able to open it up, confirm there is no damage internally, clean the bottom panel off and reassemble. If they do find damage internally, some shops will have the ability to repair at the component level, and some shops will only offer replacement of the components, which will cost a lot more money. If everything is operational though, you probably won’t need to have anything swapped.