I don't have a specific answer for you, Alkis, but I have some thoughts on it and perhaps one of them will help.
First of all, given that the Taptic engine worked with the old board (plus your having swapped out all of the relevant hardware anyway), we can be pretty sure that the problem is with the new motherboard. Not suggesting you need to, but it would be interesting if we knew that swapping the old motherboard back brought the Taptic engine back to life.
We have two possibilities to investigate; hardware and software.
With regard to hardware, I do not know enough about the iPhone electronics to know how the Taptic engine is activated and what signals are used, so the only suggestion I have here is that there could be an issue with the connector on the motherboard, since we're assuming the cable connector is good, given it worked on the old motherboard. Get out a good light and a magnifying glass and look closely at the connector itself. You're looking for bent pins, dust or debris blocking contact, any discoloration, etc.; basically anything out of the ordinary.
As far as software, swapping out the motherboard means an entirely new set of software, including phone settings, OS version, apps installed, etc. I don't know what you've done so far, but I'd personally start by wiping the phone and restoring everything back to factory settings. That should clear out any kind of software issue that could currently be keeping the Taptic engine from working.
That's all I've got for now; if I think of anything else I'll update this post. Let us know how it goes with your troubleshooting; if you find an answer it could easily benefit someone else who encounters the same problem.