Toyota Camry 2005 Sometimes Won't Start & Key Loose in Ignition Cylinder

Mom's 2005 Toyota Camry has recently not started on occasion, usually after being out in this hot desert weather. Turn key and no sound, no clicks, no turnover. Then will start up after I leave it alone for a few minutes or if I try many times varying how strongly I pull security left turn indicator or in which order I pull or turn key. Key is very loose in the ignition cylinder. I've pulled it out once while in gear. On occasion, after turning the key completely to "Locked/Off," pulling out key, all the dash lights and headlights/taillights stay on and I am able to remove key while car is parked and running. Read a previous post about the starting issue being related to a small connector behind the cylinder being broken or loose, but I would like advice on if the key ignition cylinder might be problem or if I should first run through all the potential starting issues with battery, etc.,...anythings I can try with my limited car knowledge before having to bring to Toyota.