Car won't even crank...
When it does it again, try to have someone next to the starter relay listening and feeling to see if it actuates. If not, the problem is upstream - neutral safety switch, ignition key, wiring. If it does click, you should hear the starter solenoid make a loud clunk. If not, either your starter or wiring to it is bad (ex. corroded connectors). Of course a bad ground could affect most above.
Given what has been replaced, my guess would be the neutral safety switch (NSS) doesn't know it is in P or N, probably due to wear in the shift linkage. Simple to test. Disconnect the NSS wire from the starter relay (brn wire, spade connector) and measure ohms with a multimeter from it to ground. Should be <10 ohms in "P" or "N" and >10k ohms in other gears. You don't state manual or auto and what transmission.