Vlad,
Thanks for the kind words and Happy New Year! I have had several of the 7100's recently and the tuning sections worked fine, sorry yours is not. I would guess there is another relay that pulls in to operate the tuner function is not working.
Without the schematic I would take the cover off and look at the other relays and carefully with the unit powered on feel with your finger or a wooden stick to see which one it is by the clicking sound etc. Something is not staying in contact would be my guess and go from there.
Wish I could tell you, "oh yeah do this or clean that" but I do not unfortunately.
It would bug me too if the tuner was not working
I sold both of them off recently and regret not keeping one of them, they are a great receiver.
Trouble shooting anything boils down to localize, isolate, repair. Sometimes you have to have things looked at by a pro.
Good luck with your 7100, they are a nice unit and worth fixing if you like the radio.