City sewer or septic?

You could have a blockage in the toilet itself, or it could be in the drain line. OR, if you have a septic system, it could be that the toilet fails to flush properly when the line is full due to a slow drain field.

A plunger will not usually break up an obstruction - just move it beyond the trap.

98% of the time that's all we need to do.

However, if the original clog was something that holds together (wash cloth, child's toy, feminine hygiene product, etc.) it can just push the clog downstream to the next restriction in the pipe.

When that happens, water will drain from the toilet mostly normally until the pipe back fills -- at which point it doesn't work so well. Wait a while and the water leaves the pipe and you can flush again.

This is just a working theory - the other is what Alice suggested with the septic problems or a sewer line with roots or collapsed pipe.

If you can rule out septic problems, the solution is to run the drain line with a snake. Most drain cleaning companies will run a camera down the line if they suspect something other than a normal obstruction.

Be sure to ask around about a reputable drain cleaning company. Most can come in, do the job, and and are fast, professional and reasonably priced. There are some that aren't so good though... you want to do your homework first.

jake covered it pretty well and I will just add. Start with the simple things and work toward the more involved. If you hire a drain cleaner/plumber,don't call and tell them you want your lines snaked. Tell them the symptoms as you did here,then ask them to diagnose why and reccomend resolutions.
Remove the tank cover so you can watch the flapper close during flush. The flapper should close just before water reaches the low point in bowl. If it closes early or late ,adjust the height of water level in tank so it closes a correct time.
An object (bottle,toy,hair roller,Q-tip) lodged in the bend of the toilet can act as you describe. Dip as much out of bowl as possible then remove remainder of water with a towel. Using a light and small mirror in the same fashion as a dental hygeniest ,inspect the toilet bend for a lodged object. If one is found,I reccomend fishing it out with a wire hanger rather than trying to push it through.
At 75 years old the lines are likly caked up inside reducing the size. Plumbers don't like running scraper heads because they are more prone to hang up than a small cutter head so you may have to persuade him to use the scraper if the lines are snaked.