I have owned a BRV for a few years. Replaced the battery at least twice. Never had an issue. Key remote works after battery replacement without any syncing.
Is the battery installed correctly. I suppose it must be as the little LED comes on when you press the unlock button on the remote. Suggest that you buy another battery from a reputable watch shop like Life Style or Nizam Watch co. and then try again. If it still does not work, then visit the 3S dealer.
I think your battery is CR2032 if memory serves. (my BRV was sold 3 years ago). This battery from a reputable shop is around 500/-. The same can be bought for 150 also.