So it looks like ACV, DCV, DT and Capacitance use mostly the same RC networks and internal switches in the IC. So does capacitance also not work right ? You can check the RC parts around that IC. IDK about these meters, but I'm worried it's those switches inside the chip.
Thank you for the suggestion!
I quickly tested those RC parts before but will check them again later today. The capacitance meter did show some nF without anything connected to it. So,
I think you are on the right track. With testing 1 to 4.7 μF it seemed ok-ish, maybe 20% off compared to my good Fluke 87V. But I will double check that again. I know that the 1st gen. 87 has v. limited capacitance test range.
If the internal switches are fried, then I will just use this Fluke for μA/A, resistors and continuity buzzer.