it sounds to me like its a faulty ignition switch,remember the starter solenoid is only powered up when the key is in the start position,i can understand that a sticking solenoid could cause this issue,but the solenoid cant stick if its not getting power from the ignition switch,you may have bad contacts in your ignition switch,try spraying in some graphite into the key slot run the key in and out,wiggle it back and forth ,see if this helps.but id lean towards the ignition not the starter,just my opinion,goodluck.