Pretty much as nicholas stated, though I have a logic analyzer and 2 oscilloscopes on my bench as well. Well, lots more, but you get the idea. Desoldering double sided plated through holes without the proper tools, well you'd better off just dousing it in lighter fluid and save yourself the frustration.

If it were on my bench, I'd isolate the fault, figure out which part of the circuit is responsible for that function and do a little hunting, after I replaced the electrolytics, as Nicholas suggested, you will likely find it's a simple failure of a $.10 component, at best.

The likelyhood of the bulk foil caps failing is about zero, maybe a little less.