I have worked on a lot of things with your particular problem. Pushing on the board with a stick sometimes helps but you flex the board and the problem may be across the board and somehow the pressure you put on this part of the board will fix the problem that is really elsewhere. I still do the stick thing, even if it is not perfect.
There could be a solder failure on one of the components or a microscopic crack on a trace.
Here is what I would do:
Re solder the caps, if the solder looks bad, remove it and re solder. Sometimes the through hole connections on these connections are not good and the solder does not reach the top of the board from the bottom, where you solder it.
Look for small cracks on the traces and surface mount component solder joints with high magnification.
Replace the caps (cheap enough)
It is possible that one of the surface mounted components is the problem, but less likely than just a bad connection.