The analogue bit works fine for volts and ohms.
Batteries new and the battery test function works OK. Fuses OK.
However the digits glow red as they should, but stay on zero whatever I
do.
There is a free download of the Simpson 360-2 operator's manual,
which includes a schematic, here:
http://www.simpson260.com/downloads/downloads-2.htm
I'd start looking for the presence of an output on FET Q-104
while you vary the input DC volts to be measured to the Simpson 360,
to see if the signal disappears before the main A to D chip,
IC-106. (IC101 must be good, it also feeds the analog output meter,
which you said reads correctly).
If no output from Q-104 look for the presence
of the "sample" pulses at pin 31 of IC-106
and pin 14 of IC-105.