The contacts on the starter tend to go bad and would cause a problem like this.
Check out this article - It may help.
http://wiki.answers.com/Q/How_do_you...1997_Geo_Prizm
I have a 95 and am working on this right now. This answer should apply to years 93-97.
As many of you probably know, most of the time it goes bad it is not the $150 starter itself, it's the $5 contacts (just hit 80K mi?). Good news is, these are easy to replace ... once the starter is off.