I am having the same problem as the original poster. I have tried all the suggestions in the previous posts and still get the same error as the original poster.
The installation of Surface Dock Updater v2.12.136.0 goes about two-thirds of the way through, including copying new files and registering new programs, and then aborts with the message Failed to Install SurfaceBaseFwUpdateDriver.dll
I have a Surface Book first generation, Windows 10 Pro Version 1709 OS Build 16299.334, Surface Dock Model 1661
Current registry keys for Dock firmware are
Component10CurrentFwVersion 76661360
Component10FirmwareUpdateStatus 5
Component10FirmwareUpdateStatusRejectReason 0
Component10OfferFwVersion 76661360
Component20CurrentFwVersion 76634736
Component20FirmwareUpdateStatus 5
Component20FirmwareUpdateStatusRejectReason 0
Component20OfferFwVersion 76634736
Any help would be appreciated.