I found the problem with the hp 8904A keys. A ribbon cable connecting the front PCB to the top PCB in the main chassis. I re-seated all the cables at first but the problem didn't go away. It did change a bit in that some keys that were not working before started to, and some that were - stopped working. So I was onto to something. Then I bet the money on J1. I remembered looking at it that I wasn't very impressed with the choice of cable connector when I took the whole thing apart after I first got it.
I have never seen that selection of cable and connector in any other hp gear - have any of you? I don't know how the end with the pins was made, it doesn't look like an end connector that you could make a direct replacement for at home. Looks like it was fabricated at the connector factory and shipped to hp ... ? Anyway it may have been the first and last time it was used by hp, and for good reason.
Anyway, I pulled the connector for the second time, and cleaned it with alcohol, and wiped with some contact enhancer, and the second time it was fixed.
The hp 8804A Multifunction Synthesizer is an interesting bit of kit though. It has four channels internally - each one can be set up to generate a certain waveform (freq,. amplitude, phase, and type (sine, square, noise, etc.). Then these channels can be combined together internally to make any sort of output you want. In fact, had to glance back at the operations manual to remember how to get it going after three years. The fact that only some keys were not working made me think I was not doing things the way it wanted. Pic shows sine and square wave with noise intentionally added.