Here is my final attempt to install the drivers and only to realize that Microsoft decided to fool the customers and if your type cover is not working, it is most likely intentional to force you to buy the next model or to make you believe it is a hardware issue.
Yesterday after discovering that my driver folder under system32 does not have SurfacePro4TypeCoverIntegration.sys file needed for the keyboard to work, I was able to get the driver package (inf +sys+cab files) and tried to install the drivers manually into my SP4 (device manager>action menu>add legacy hardware> install the hardware manually> have disk> select the SurfacePro4TypeCoverIntegration.inf) which gives the error "the folder you specified does not contain a compatible software driver for your device. if the folder contains a driver, make sure it is designed to work with Windows for x64 based systems".
driver package location - **removed link to 3rd party site hosting Microsoft intellectual property. Microsoft files and drivers are not redistributable**
This looks like the end of our hope. the x64 drivers made for SP4, are not compatible with our devices. Interestingly I found "surface3typecoverintegration.inf_amd64_be4dfba7097178de" folder with SP3 drivers at C:\Windows\System32\DriverStore\FileRepository which might explain the type cover incompatibility.