My car will not start when I turn the key. Will not even crank. New battery, alternator and starter. Gauges and light work when key is on. What's wrong?

Question edited for clarity.
Question moved to model category.

Did you disconnect the battery when you changed the starter over? Then did you reset the alarm and engine immobilizer?

Reset information

https://www.google.com/search?q=2007+chevy+equinox+anti+theft+reset

2007 Nox won't start after battery removal

ChevroletForum https://chevroletforum.com > ... > Equinox
Apr 13, 2017 - Equinox - 2007 Nox won't start after battery removal - I had a noise I thought was an alternator wine. Voltages looked marginal, but good (14.6V charging, ...
change battery no start no crank - Chevrolet Forum
Apr 13, 2017
2009 Equinox won't start after battery disconnnected
Apr 13, 2017
2008 Equinox won't turn over after ECM removed
Sep 30, 2017
Starting problem (continually turning over) - Chevrolet Forum
Apr 13, 2017
More results from chevroletforum.com

ANSWERED: No crank no start (Chevrolet Equinox)

CarGurus.ca https://www.cargurus.ca > Discussion-t35502_ds797539
13 answers
Weak or bad battery, bad starter or poor connections or corrosion at the battery and or the starter.

problem can be loose battery terminals
dirty battery terminals ( must be shiny clean on both terminals and battery posts) loose battery connections
bad battery ( have a load test done on the battery)

check the solenoid switches in the black box under the hood

Clean and tighten battery cable connections and check battery ground, engine ground-should be a ground strap from engine to the body or frame. If this happens and you have nothing, no headlights, nothing-it's almost certainly a problem at or right off the battery.

What happens when you turn the key to on? Do the warning lights and gauges come on? Turning the key to start, do the lights and gauges stay on? Just nothing at the starter?

Or does power just shut off when you turn the key to start, everything goes out, no warning lights or gauges? Then check cables, battery terminals, grounds for clean tight connections. There is a problem between the battery and the ignition switch.

If the switch still receives and sends power out (to the dash, for one) but start circuit is not working (from battery to ignition switch to clutch switch to starter relay to starter solenoid to starter to ground-and back to battery), then here's where we at: with key off, use a small screwdriver and short the big cable at starter to the starter solenoid small wire connection, or use a small jumper wire to do the same-battery cable at starter to the small wire connection on the starter solenoid. Starter motor should spin and crank engine. Does it? If so, start checking the start wire out of ignition switch for power when key is held in start. If you have a clutch switch, check for power in with key in start. Should have battery voltage to the clutch switch with key held in start. Keep checking the start wire along the start circuit. Not sure how the start relay is wired into the circuit, would have to see a diagram, but if you pull the relay out and use a test light or multi meter, could check for power on the terminals where relay plugs in. Key off, should have one terminal that is hot. With key held in start, at least one other terminal should also be hot. This would be the start wire out of ignition switch sending a signal to the relay.
Good luck, hope you find it. Sorry I don't have a wiring diagram to help you more.

Do warning lights and gauges come on, when key is turned to on?
If yes, check for power on the small wire at starter solenoid mounted on the starter with the key held in start. If power at the solenoid, take starter off and test for a bad starter or solenoid. If no power at solenoid when key held over to crank, work back to the switch in the start circuit-starter relay, clutch or neutral safety switch,-power from the start wire out of switch is not getting to the starter solenoid.
If no warning lights or gauges work with key in on position, power is either not getting to switch (bad maxi-fuse or fuse link, or bad battery connections-clean and tighten, recheck)-or the switch itself is not sending power out. Check if battery is charged up. Check all connections and grounds for loose, poor connections.
The start circuit starts at the battery, then to ignition switch, then out of ignition switch on the start wire to the clutch switch (or neutral/park on automatics), and on , ending at the starter solenoid on the starter. Somewhere in your starting circuit, power is lost. Start at the battery-check charge, check connections, check ignition switch.

Won't turn over or won't start?

Has to turn over fairly fast

Check for fuel pressure & either spark or
injector pulse while cranking

Well, that's good, but even if the chain was broke, the starter would still be tryiing to start the car. Since your starter wont crank the engine over, your start circuit has a malfunction. Possibly the starter went out, so you need to have that tested for a malfunction. A simple test of part of the circuit is to turn the key to on.. Now your dash warnimg lights (oil, alternator, and check engine light) should be on. Are they on, and your gauges working? If not you have lost power to the ignition switch, so check your battery connections. If the key switch turns the dash on, then turn key to start. Do you hear a click from the engine area? If not, have the starter checked. If you do hear a click, or several clicks, then power from the switch is causing that click, probably at the starter. Turn the headlights on and observe them. Are they bright? If not, charge the battery up. If they are bright, watch them while a helper turns the key to start. If the lights go dim in start, probably a bad starter. If the lights don't dim, it could be a bad connection somewhere, like the battery or starter. Good luck

more then likely its a bad starter. or the cable to starter.

Sounds like a classic case of a dead battery. It takes much less energy to sweep the gauges and turn on the lights than it does to crank the engine over. The clicking noise is usually your starter solenoid trying to engage and spin the starter. Try a new battery. Happy motoring.

Good luck.