I bought a asus refurbished laptop, what should I do about charging a battery,charge it for eight hours without turning on the laptop??

A battery will charge as you use it . Go aheead and plug it in go about your laptop use as normal it does not need be off to charge the laptop any faster
Its using AC power to run and will still charge the battery
IF it does nto charge in a few hours it could be a weak battery
Try this first beofe you bring it to a service shop EBAY sells every type of battery ever made & Cheap too ! but check for warranty in EBAY bought battery look for return 100 percent guarantee on battery sales