Just an update to say that, in the end, I was able to fix this programmer.
The culprit - two partially dead MC74HCT273AN octal flip-flop ICs.
The behaviour of the unit when I first checked it was that most of the tests in the self-test were failing and, at the end, the programmer would stop responding.
In absence of any servicing info, I tried checking the more susceptible components, starting with the bottom board.
This one has the power supply section, as well as the main processor, an SRAM IC, one EEPROM and one FPGA.
And, since running the self-test while connected to a PC did recognize the programmer and it was able to check that the SRAM was good, I concluded that most of these components are likely to be fine.
I also swapped the FPGA IC between the bottom and top boards and I could see no difference in behaviour (so, either both were bad, or both were good).
In any case, after some more investigation, I concluded the bottom board is most likely ok.
Next, I focused my attention to the top board, which is full of ICs and transistors.
Checking the transistors was straightforward, but the ICs were a different story.
So, I decided to desolder all of them and try to check them individually.
I used this opportunity to install IC sockets, so I could remove/swap any ICs on the board easily.
Checking the ICs one by one, I was able to identify the two broken ICs.
After replacing them, running a self-test worked all the way through, with no errors reported.
![ThumbsUp :-+](https://www.eevblog.com/forum/Smileys/default/icon_smile_thumbsup.gif.pagespeed.ce._JElyJQqdB.gif)
I also did some EPROM and EEPROM reading/burning checks against my otherwise trusty TL866II and all is good.
![DMM :-DMM](https://www.eevblog.com/forum/Smileys/default/smiliey_dmm.gif.pagespeed.ce.CvRqtDiING.gif)
Ok, not a multimeter, but you get the idea.