Mike - as a Toyota derivative your Geo is most likely equipped with a Nippondenso starter. These starters are subject to a common, but fortunnately simple problem. On the starter solenoid should be a large cable (this is B+) and a smaller wire, which is the signal, or activation wire.
Take a simple 12V test light and check for power at the large cable - this tests your test light connection. Now, while someone tries to start the car check for power on the smaller terminal - if the car doesn't crank but you have power the problem is internal to the starter. Another way to test this is to GENTLY tap the starter while trying to start - in most cases the starter will engage.
If these symptoms are present the easiest solution is to replace the starter. However there is another way in most cases...
After removing the starter carefully remove the end cap from the solenoid (the part with all the terminals). Inside the end cap, and attatched to the B+ terminal, should be a large copper contact. This contact wears over time. In most cases you can loosen the nut and simply rotate this contact so that a new, unworn section is used. Other times the contact must be replaced. Obviously for mush less than an entire starter.

Good luck - hopefully this works for you

Gregg

P.S. - this repair also applies to any other car using Nippondenso starters - Geo, Toyota, Honda, Nissan, etc