Wierd starting problem

HI I bought a 96 auora a few months ago and ive been having nothing but problems. Lately it just wont start. All the electronics, lights, ac, and so on come on but there is no sound coming form the engine. Sometimes if i come back in 10 minutes it will start up, sometimes it wont start again for a week. DOsent seem to be any reason for when it does or does not do it or how long it takes before it fixes itself.
Once i had it towed in from my home where it wouldnt start then it started for the dealership right away, and they said they couldnt do anything now that the problem went away "for now." BUt they still charged me $100 for do nothing besides the tow and "checking over". Any thoughts on what the problem could be?

not even a "click"?

first the free stuff...

check all battery and ground connections - follow all the wires and check all connection especially the connections at the starter.

the next time it is reluctant to start, give the starter a tap and see if it then starts (bad starter)

my next thought would be ignition switch...

So not even a "click" under hood when you turn the key? And everything is working later? Solved the same issue week ago. if there´s total silence, then starter solenoid is failed.
One thing you can try - disconnect starter solenoid cable connector on the engine. It´s located at right back side on the top of the engine just behind the cruise control module (There only two wires going under intake to the starter - you know that starter is under intake? - front one is the battery power cable and another is solenoids power). Turn on ignition and connect extra wire from underhood battery terminal to the starter´s side of disconnected connector just for try-up. Then may happen that engine cranks, and if you reconnect wire, after that it works again awhile. If it so in your case, then it is repairable. Cause of this action is what i call is bad engineering. Point is that solenoids pull-in winding is getting his ground from copper bolt on solenoid back. Problem is that bolt is tightened to case (pull-in windings contact is between them) with very thin 2mm sheet nut and there´s not enough tension. So contact gets dirty. You need to remove starter, remove lower sheet-nut on solenoid, clean surface and install regular nut there. Then it will work fine again.
Another option is, if you dont want to mess, just install new solenoid... and if you really dont want mess, install new starter.

oh, forgot to mention - when you disconnect starter solenoid cable, you must also check out if current presents here. For that connect bulb or voltmeter between this contact and body and turn the key to START position. Bulb must light up or voltmeter show some reading. If t´s not, then your problem is somewhere else, sorry.

also may be key put the key in and try to start it if it will not start leave the key in the on position for a few sec and see if it gives you a message clean key wait 3 min. if it does this is part of the security system good luck