If I suspect that a battery is going south on me, I'll do sort of a quick and dirty load test of sorts by reading the voltage at the battery terminals while cranking. [edited to add: The battery should be reasonably well charged prior to performing this test.] With suitable test leads and clips, it can be arranged so that the digital multimeter is easily read from inside the car.

A battery that looks fine just sitting there may show a large voltage drop under the load of cranking the engine. If it looks fine at the battery terminals, but the cables are suspect, then one can do a similar test at the starter terminals to find out what voltage the starter motor is seeing (again, during cranking, because that's when a voltage drop due to dodgy cable or connections is apparent).

I also agree with others here that the original battery is the prime suspect based on advanced age.