Depends upon how critical the laptop is in your situation. In most cases I would not buy it. Usually they cost about 15% of the original list price of the laptop for each years extended warrranty.
A small percentage of the laptops have hardware related failures. The odds are in your favor unless you drop it or travel with it a lot. If you can write it off as a business expense that might make the cost more appealing.
So, figure out how much it will cost and figure in 2-3 years new laptops will most likely be less expensive or at least the same price with more features. In most cases, unless the laptop is critical to your day-to-day business I would not spend the money.
You could borrow a battery from a friend and see if it charges their battery or buy another battery and see if it is charged by the AC adapter.
You should test the ac/dc power charger with a digital multi meter (DMM) and see if you have any DC voltage coming from the pack… if not replace.
If the AC charger works then my guess is that there is a faulty solder connection on the system board where the AC/DC power connector connects.
You can get a cheap DMM for $5 or less these days
Sigh. Next time don't have your water or coffee or coke near your laptop. It will be most unhappy.
If it is water you will be more fortunate than if coke or coffee. If it is plugged in turn it off. If something is obviously wrong turn off the laptop. If the AC adapter got wet and the battery wipe them off. They may be damaged. Remove cards in the PC slot and dry them carefully. Clean the liquid off the display. Remove the memory module and dry it. If it is the keyboard remove the affected keycaps and dry and clean them. Once it is dry then turn it back on and see what happens.
You might be lucky and all the extra work might be a lesson learned and you might not allow liquids and your laptop to mix again by keeping them far away from each other. If not you might have to call your local laptop repair shop and spend the $60 to $70 to have the problem diagnosed. If you fried your motherboard you will be most unhappy as you might have to kiss your laptop goodbye. A $300-$400 repair might not be cost effective.
I hope you had your data backed up.