Yes, it's far more likely for a chip to fail in one section when it is an analog type device. Even digital stuff can lose a single stage or line. But op amp chips will fail in one stage, not that common for them to fail completely (but that happens too).
I agree with Gordon, and I've said it before, I shall say it again.. replacing cap's is not a good strategy because a) cap's are actually quite stable if manufactured from 1970 onward and b) replacing all caps may actually make the fault worse by confusing what was originally wrong with an error made while replacing all cap's.
Not wanting to offend anyone but only those that don't know much about electronics say that cap's are most likely at fault. In my experience, there are just too many different ways for electronics to fail to be able to blame cap's first. The exception to that is when working on equipment that is pre 1960's (1960-1970 is a transition era which I won't go into). Anything pre 1960 is going to be using older cap designs using some scary PCB's and stuff that oozes out with the appearance of crude oil and will often smell worse. Those cap's are most certainly the most likely problem. Pre 1960's valves, resistors and coils are incredibly stable components from that era with the exception being the capacitors. By all means, the first thing to look at in 1960 and before kit will be the capacitors. And, since alot of that valve kit is high voltage stuff, you damn well better replace those cap's unless you want a seriously nasty chemical fire in your workshop/home/business.
But anything from 1970 onward is just not going to have that kind of problem certainty. So your best approach is to FIND THE ACTUAL FAULT. No blind man parts replacements. Please, I beg of you.
/Mike