[ischmitz]

According to the data sheet pin 18 and 19 are the input and outputs of an inverting amplifier of the 8051. With the quartz and the capacitors in place this should produce the clock signal. If you have the right equipment you can isolate pin 18 by removing R720 and feed a 6 MHz clock signal into pin 18. Short pin 19 to pin 20. If that still doesn't produce signs of life the 8051 is bad.

You might be able to check pin 18 and pin 19 with a high-quality DVM in diode mode and compare it against the good DME. However, I'd caution that these older 8051 are not as rugged as current devices and the last thing you want is to kill the second unit in the process. So proceed with caution and fully understand the data sheet, the absolute maximum ratings and your test equipment.

You can desolder the capacitors and replace them (easy) or test them with an LCR meter but it is virtually unheard of that these go bad. Same for the quartz, replacing it is straightforward but I don't know how to test it short of having a vector network analyzer. And for the price of one of those you can probably buy 10 new DME units....

Also the quartz going bad is not a common failure mode and highly unlikely, especially due to a short on the analog board. It is more conceivable that the +5V rail took a hit when you shorted things and that killed components on the logic board powered by +5V (MCU, ADC, EPROM, glue logic).