If you mean the starter does not run and the dash lights do not dim while trying, verify that the ignition switch and PNP switch are in good condition. If either is bad wiggling the key or gear shifter may cause the car to start and you will have identified the problem.

Do you mean the trip reset button? What's the reasoning about this? Maybe if the ign switch or wiring are uncertain you jostled something unrelated to the button when pushing it?

If the starter does not run, runs weakly, or clicks, and the dash lights dim while trying, you should verify the primary wiring (battery, alternator, starter). Even if battery is new something might possibly have been disturbed during installation or testing, or the battery may have a manufacturing defect. I once had a new one with a positive pole that separated from the plates inside the battery and made intermittent contact (though you would see no dash lights if that was true).