1996 Honda Accord car will not start

Do you mean it cranks over and refuses to start, won't stay running or won't crank over at all?

Could be your security anti theft control unit if it has one/security starter cut relayignition switch/transmission gear position switch ans starter.

Have helper hold key at start position and check for power at the starter solenoid black and white wire-power there-replace the starter-No power backtrack to the other components I've mentioned-