Here is another SBC RU-950 success story. After the typical chain of events (screen buttons not responding, re-flashing, calibration error) I've tried first cleaning the contacts of the ribbon cable at the PCB side, then rubbing the four contact points on top of the touchscreen. It didn't help. Then I've pressed on the contacts with a needle in a couple of points and voila- it worked! Hopefully it will last for some time; if not, I'll detach the cable to experiment with some conductive glue. Thanks guys for your excellent hints!

P.S. My previous remote (SBC RU-940) died after 3 years of use with a (try a guess) contact problem which looked like a microscopic crack in a PCB. Some wise guy said that electronics was a science about contacts...