More than likely, the main relay (located near the hood latch) is the culprit. The solder cracks on a few contacts. They can be re-soldered. One way to tell is by banging under the dash when it cranks but won't start. It's also possible that the ignition switch is at fault. When starting, hold the key in the "run" position. Parts are available for both issues.
My "free" 92 LS