First try a two button reset:
Step 1: Press and hold the power button on your Surface for 30 seconds and then
release it.
Step 2: Press and hold the volume-up button and the power button at the same
time for at least 15 seconds and then release both.
The screen may flash the Surface logo, but continue holding the buttons
down for at least 15 seconds.
Step 3: After you release the buttons, wait 10 seconds.
Step 4: Press and release the power button to turn your Surface back on. You
should see the Surface logo.
Second, after the above, please go to device manager and see if both the Marvell
wifi network adapter and bluetooth are present and if wifi is still not working,
see if there are yellow bangs and reply with the error codes.
Third, if a driver is missing, to verify you downloaded and ran the correct
installer, please go to
https://www.microsoft.com/en-us/download/details.aspx?id=38826
and download SurfacePro3_Win10_10586_1702002_0.msi on a different computer and
transfer it to your SP3 on a USB stick. then run the MSI file to run the
installer. This will install drivers and firmware.