Dealing with Microsoft the corporation is fraught with difficulty unless you have a support arrangement up front. Your best bet is to contact a retailer/reseller of their hardware and ask for a recommendation for a repair shop, if you're lucky the salesperson may even offer free advice. Battery replacement shouldn't exceed $200 if the repair shop is honest - most of that is labour.
Funnily enough Microsoft did listen to me once when their myapps cloud site asked for my feedback. I gave them a big serve about important features that were lacking in the experience and about three months later they magically appeared - for the better.