I'd still have to double check the battery. Use a digital multimeter across battery posts, everything off. The generic spec for a full charge is around 12.6 volts. Leave the meter leads hooked-up to battery, have helper turn key to crank, watch the voltage, how far does it drop or does it drop at all?
Check for voltage at starter solenoid s terminal with key in the crank position. It should be hot. Terminal B should be hot all the time. Any testing at the starter, make sure the tranny is in park or neutral and the parking brake is set.
Check for applicable trouble codes. Your security system could be an issue? To check for codes, at the least, you need an obd2 code reader. Your local autostore should have one.