Faulty MAX134CMH+D A/D Converter?
Try to duplicate waveforms in figures 6,7 or 8.  If you have no scope use your Aux-in Audio port and get the free scope S/W.  DMM Clock is only 32kHz. (if you really can't find the SW, buy a new DMM.)
I suspect it may be related to the periodic Auto Zero Integration Phase which is showing all FFFFh as full scale 4.000 which you should see periodically on above. It matches the display change rate. Then dig deeper.
My SWAG debug methods include wandering my finger around all the traces with other hand grounded or open to add capacitance or crosstalk between two fingers or shunt stray noise or bridge cracked solder joints.