Definitely not the best “refurb” I have ever bought.
Computer is function while the battery is DOA. the “shivnet” warranty the shipped with the computer (somewhat different from woot page link) does not cover the battery, where they state they “check the battery to make sure it charges” whoever checked this one should probably go do something else 
not worth returning. replacement is probably less than the cost to ship. Guessing the distributor’s motto is “we put the shiv into shivnet!”
If you haven’t done so already, contact Woot Support to see if they can help you out on the warranty aspect.