Hi and welcome to the forum!
It sounds like something is loose. Think about what you said. It is fine with the key in the ignition, (by that I mean turned to the on but not run position?) and when you start it up it does that. It sounds like when the engine is running, a vibration might be making a wire or terminal or ground go intermittently open. Do you have a factory service manual, better known as an FSM? I have a 94 so I do not know if the wiring diagrams might be related.
Another thing to think about is corrosion. If it spent its life in New Hampshire (I used to live in Boston but I'm okay now :L) and if it was anywhere near the coast the salt water in the air can raise riot with electrical contacts.
When you say dash do you mean the speedo display? Or something else? See if there is something related.
I would try to do as much as I could without tools first. For instance, you could remove the fuse for the A/C control and see what happens.
Best of luck and keep us informed.
Paul