'91 Camry Won't Start

My '91 Toyota Camry will no longer start, or even click when the key is turned.  All electrical comes out without any issues.  We had been experiencing some intermittent issues where the car was not turning over, but would end up starting after a couple tries.  We had taken the car to Autozone to have the alternator, starter, and battery tested, and ended up replacing the battery as that had tested bad.  Car worked fine for a while, but now won't start after many attempts.  We also have been having problems with the ignition the past couple months, where the key is able to be removed from the car while operational, as well as the ignition always acting as if there is a key inserted (dinger sounding when door is opened, unable to lock despite no key being in place)  Is this potentially just a replacement of the ignition cylinder/tumbler, or is it most likely something more complicated?