First of all, don't rush into repairs at the first service you find and don't pay for anything right away. The battery might not be charging for different reasons - it's not necessarily the battery itself that's the problem. It could be the connector, the charging controller, or the adapter. Different issues = different costs, so you need to figure out what exactly is broken first.
Call the official Asus service center and ask about the cost of diagnostics - they often do it for free or for a small fee. After diagnostics, you can decide whether the repair is worth the money. At the same time, check the cost of parts and labor at regular service centers (not official ones), it might be cheaper. If the repair comes to half the price of the laptop, it might be easier to sell it as is and buy a new one.
One more thing: if the laptop has been used in harsh conditions (constant overheating, frequent drops, liquid damage), the battery could have failed earlier than expected simply from wear and tear. That doesn't mean you're owed anything, but it's worth knowing. In any case, get diagnostics first, then make your decision.