Yep, the cap replacement worked. I pretty much replaced anything electrolytic in the whole thing with identical caps. It's been a while, but I know I had one definitely bad one, and I think several others were questionable on the ESR meter. But at the point I'm replacing electrolytics, I'm going to replace them all.
Once the replacement was done, the unit popped up and started working.
I had two additional issues that I can recall: One of the knobs was difficult to turn and another just twisted on the shaft, I discovered that knob was pushed in mechanically too far on the one and the other was just loose. I seem to recall that the knob had a cap you popped off to access the screw which tightens the knobs.
In the process of troubleshooting the above, I killed one of the 40 pin IC's (obsolete GPIO of some sort), so I had to procure one off the internet. Frustrating to kill an instrument you've almost got working, but once I got the replacement everything worked fine. I've been using it as a calibration transfer source around here (get a DMM Calibrated, then use the DMM to verify calibration the 2701C, then calibrate lower resolution DMMS with it.).