Purely based on speaker age and some research that suggested for the age, the capacitors typically have run their course. And since both woofer and tweeter are not working, I was thinking it must be this. If there are better tests to rule that out than I can definitely do that.
A lot of people recommend replacing caps but in speakers, they generally don't fail unless someone fed it too much voltage and in that case, you can usually see that the cap 'exploded' or bulges at one end.
How are you testing the speaker? You can use a digital multi-meter to test the tweeter for continuity and if that's successful, you can just connect it to the other speaker's wires for the tweeter- if it works, you know the tweeter is good. Test the wire's continuity from the terminal on the cabinet to the point just ahead of the cap- if you have continuity, it's likely that the cap is bad but you can test that with a meter, too- set the meter for testing Diodes and connect the probes to the cap's wires- you should see high resistance and the value may change. Reverse the probes and test it again. if you see that it's open, replace the cap.
Parts Express has caps- you could use a 2.2uF and a 1.5uF in parallel- if you change the crossover in one side, do the same for the other.