Battery connections all good? Use digital multimeter across battery posts, everything off, what is the reading? With meter leads still touching the battery posts, have helper turn key to crank, how far does the reading drop or does it drop at all?
Note the diagram, pull starter relay, use jumper wire in two cavities for switch side of relay, right side in the diagram, line with arrowhead. The starter motor should crank the engine. That doesn't mean it will start. At least you know the starter motor will crank the engine. If you try that make sure tranny is in park or neutral and parking brake is set.
When battery voltage is lost, sometimes, some systems need to relearn or be reprogrammed. I haven't looked at your security system? Any applicable trouble codes?
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