Too bad, you wouldn't believe how often PCB cleaning will get rid of odd readings.
It's fortunate you have an 8600A. It has a feature that is useful for debugging DMM front ends. On the 200mV and 2V ranges, it's impedance is over 1 Gigohm. The usual DMM 10Meg impedance is too low for the downstream side of a DMM voltage divider.
Set the 85 to VDC and short the inputs. With the 8600A in 200mV range, measure from the COM jack to the second pin up from the bottom of Z1. It should be very close to zero.
Now apply 10V to the 85 input. It should auto-range to the 40V range, so the voltage divider will be in 1/100 mode. You should now measure very close to 100mV on the same pin of Z1.
If your measurements show too high a voltage at that pin, then there is some current leaking somewhere that is pulling the ADC input up, causing a problem.