2005 Chevy Equinox will not start

Use a digital multimeter across battery posts, everything off. What is the reading, should be over 12 volts. Leave the meter leads hooked up to the battery, have helper turn key to crank, how much does the reading drop or does it drop at all?

You can try to jump the starter relay in underhood fusebox. Use a jumper wire on the load side of relay, in the diagram, the load side of relay is the side with the arrowhead. When relay is energized that line will move to the other terminal and carry voltage to starter solenoid S terminal. Any testing, make sure tranny is in park or neutral and the parking brake is set.

The starter should be located down low on the driver side.

Just to add, if your security system has problems, even if you crank it, it won't start. I haven't looked at the security wiring.