Replace It and Do It Right
Since the toaster works OK elsewhere, the problem is somewhere in the receptacle. Truly diagnosing it would take as long or longer than simply replacing it, and it isn't worth the $2 that a basic replacement will cost.
In a 35-year old house with original wiring, you most likely do NOT have GFCI circuits or receptacles installed. While you could argue about an absolute requirement for a straight replacement, the kitchen is one of those places where GFCI absolutely makes sense - simply too easy to have a serious safety problem that a GFCI will protect. So unless you have upgraded your breakers to include GFCI, replace the bad receptacle with one that includes GFCI protection. That will cost you more than the basic $2, but it is well worth it, particularly if some day you have a problem with that toaster where the toaster is the problem instead of the outlet and your hands are wet or you (foolishly, but people do it) get toast stuck and try to get it out without unplugging the toaster first, etc.
Note that there is one possible complication with installing a GFCI receptacle. If you currently have power chaining from one receptacle to the next, which is quite common (and perfectly safe), and the existing receptacle has one set of wires on each side of the receptacle, you can't simply copy the configuration to a GFCI receptacle. On a GFCI receptacle, one side is LINE (must be connected to incoming power) and the other is LOAD (for connecting to additional receptacles). If you are not 100% sure then you should connect all the blacks (hot) together and all the whites (neutral) together and use a pigtail (a short piece of matching wire) for each one to just the LINE side of the new receptacle.
Use the screw terminals on the sides rather than the "back stab" connections in the back. Much easier for a novice to make sure you have a good connection and less likely to have a problem in the future like the problem you have right now.