Engine wont crank over

No snapping blue spark continue to troubleshoot the ignition system-power input to the coil/coil packs, coil's resistances, distributor pick-up coil, ignition control module, cam and crank sensors and computer Note: If it doesn't apply disregard it.

No crank at all/nothing/nada when key is engage to starting position

Could be the starter, starter relay, park and neutral switch/transmission position switch and ignition switch assuming the battery and connections are good. Note:If it doesn't apply disregard.

Since you just changed the transmission and it wont crank it may be a bad neutral safety switch or prdrnl switch.

Best thing to do is go under it and see if all the wiring connectors are hooked up.

Will it crank in neutral?

Next time it refuses to start-Lets do below for a start to determine if its fuel or spark related issue and get back with some results

Get a helper disconnect a sparkplug wire or 2 and ground it to the engine atleast 3/16 away from ground-have helper crank engine over-do you have a snapping blue spark? If so-you have a fuel related problem, check the fuel pressure to rule out the fuel filter/fuel pump/pressure regulator and listen to the injector/s are they pulsing or hook up a noid light. No snapping blue spark continue to troubleshoot the ignition system-power input to the coil/coil packs, coil's resistances, distributor pick-up coil, ignition control module, cam and crank sensors and computer Note: If it doesn't apply disregard it

Check all main fuses under the hood. If you are not getting power to the ignition switch, there has to be a major break down there.

No crank at all/nothing/nada:

Could be the starter, starter relay, clutch switch/park and neutral switch and ignition switch assuming the battery and connections are good.

Check and test the idle air control-auxillary air control valve and the fast idle air control valve-also check the cold start injector if it has one-