Hi,
I recently acquired a 7704A with a similar, if not identical issue.
Since keeping it on for a long time was not a good idea, with scope in OFF state I measured resistance of all power supply outputs; +15V was a nice short. Step by step I isolated the responsible area as the MAIN INTERFACE. Eventually I found C2085 (in perfect looking condition) as the short component. The part list says it's an electrolytic capacitor - in my case it was a Tantalum. I didn't have a Ta and I replaced that with an Al, 100uF/25V, and that solved the issue.
Hope that helps
T
