Hello Chloe,
I'm Alexis an Independent Advisor.
There is not much more that you can do here after resetting the device like you did.
I'll advise you to contact the after-sale service of the place you bought the Microsoft surface wireless adapter.
If you bought the Microsoft surface wireless adapter directly from Microsoft, go to this link :
https://account.microsoft.com/devices/
You will be able to make use of your warranty.