No Power to Ingnition switch

I have an 84 Cherokee, after you drive around for a while and then stop the car, if you then try to start the car about 5-15 min later when you turn the key on the car acts dead. Radio/blower have no power. Accessory position is dead too. Inside light work fine and head lights are bright. Wait about 20-30 min and it works fine. Ignition switch has been replaced.

Any ideas?

I'm not sure on the 84 but I would think its the same as my 89, I would follow the wire from the battery to the starter relay where all the power wires connect to the one terminal, disconnect battery, remove the wires from the starter relay from the big post and clean + tighten them up. Even the starter relay is only about $15 dollars to replace. Also wonder if the ignition switch is adjusted properly. Really does sound like a bad ignition switch though.