The symptoms you describe could be caused, as you point out, by several different things.? Personally I would lean towards capacitor issues as a "first check" item - I've worked on 12 of them so far (and am waiting for #13 to arrive) and capacitor issues have been the most frequent cause of problems.? In the 3400A the power supply capacitors often go bad but there is really not much required of them so, even faulty, they usually still work "good enough" - and the rest tend to be used in ways that leakage can cause numerous and fairly subtle errors. And each of the boards have multiple revisions, each of which changes what tends to go wrong.? Throw in a handful of carbon comp resistors and you get a whole other avenue for issues to crop up.? All that being said, I love working on them and have have had the best luck with starting off by replacing all the electrolytics on the power supply board then just trace the signal through the unit.? The troubleshooting steps in the manual - provided it actually addresses your particular hardware combination - are, as typical of that vintage HP, very helpful.? While I've not personally had issues with it, I have heard from others that the input JFET can get leaky and cause problems.? Don't know if that would result in your issues but it would be something to check.
On a side note, one of the very first things I do is replace the output jack on the rear with a BNC - makes later adjustments *much* easier and any other use in the future.
Hal
Harold Foster