Clutching at straws here, but, one small difference between the faulty unit and the known good unit is the faulty on has the 04C option (basic crumby 10mhz) and the known good one has 04T option (better tcxo with oven?)
04T is just a TCXO, no oven
04E is the high stability oven - you want this if you can get it
04A/B are the standard OCXO options, the A being fast warm up and B being slightly more stable.
04C is a basic crystal, intended for use with an external standard
Maybe, although the eproms look identical and have the same software ver. Maybe they are still programmed slightly differently, maybe when it boots up it checks the accuracy and/or stability of the internal 10mhz ref. The eprom from the working unit will be expecting to find the oven tcxo quality ref, and when it doesnt it sits and waits for it to settle down before allowing measurements to take place. Hence apparently freezing/not booting.
Will try swapping over the oven tcxo tmoz and let you know. Long shot but you never know.
Unlikely - the oscillator in these just sits on a separate board at the back with a connector that carries power and the 10MHz back - there's no way for the CPU to know what type it is.
In fact I'm pretty certain the firmware is the same for all the 199x counters - it works out what model from which front panel is present
Oh, it's worth replacing the PSU caps in these models, they are a known weakness especially the big 680uF ones.
I know you said power rails were OK, but double check them for ripple.