I have not read all the other responses so apologies if this is a repeat.
I owned a 744 once with the same hiccup behavior. The CRT driver circuit was bad. You report that you have (had) good VGA from the back panel, and that's what I had.
I was able to temporarily remove the connector to the CRT circuit (I believe it was a small four-pin connector) and then the scope powered up and I was able to use it with the VGA output.
After that I was able, some how, to troubleshoot and repair the CRT board, but I see someone has offered to help with replacement boards so that would be the way to go.
Good luck and of course keep us posted.
dan
