I had the same problem with Redmi 3. I bought it online and it came with a re-seller ROM which is why it could not be unlocked.
However there is thread on the redmi 3 official forum entitled Redmi 3 Fastboot Guide and it was a life saver.
Follow the instructions exactly, and it will work. Despite the title it does not use Fastboot, so do not boot to fastboot, but read the instructions carefully for the way to boot the device for this procedure.
It will work with a locked device, it did for mine.
I now have my phone unlocked, rooted and with MI8 rom from this site installed.
For those who maybe experiencing no SIM detected, this will clear up that problem.
My phone is working like a dream, thanks to the great guys who did all the hard work both on this site and in the thread above.
Unfortunately I cannot post the link because of forum rules.