They sometimes look OK until you remove them and the leads fall off :) After 35years they are well past their life expectancy and are probably not performing anywhere close to their specs.
Usually you can see visible corrosion around the area of the cap where they have outgassed and eaten into nearby leads and usually the tracks on the board. Others have possibly leaked but the internal gel has dried and turned to a fine dust that looks innocuous. You may find a mess under the cap when it is removed. Generally as a rule of thumb I would replace all the caps and the internal battery just to remove any possible issues with the power supply before looking for other faults. Although it sounds like this unit just has bad caps everything else seems to run OK. <snip> > None of the existing caps looked visibly damaged or leaking. <snip>
