YUKON Starter Problem - Help!

My '94 Yukon has been having an intermittent starting problem. Turn the key and nothing, just a single click of the solenoid(?). I cleaned the battery terminals and same thing. I believe it is either the ignition swithch itself or the "Park" activator switch on the column shift. Another alternative is the solenoid, but one day I was able to activate the starter by holding the key in the start position and puting additional pressure towards the "Park" setting on the shifter. But now that won't work either. I'm not sure where this switch is - at the base of the coulum near the floor, or somewhere in the steering wheel area. I hope it's not under the truck where the shift levers enter the tranny- because it's cold out here!
Thanks for the help! TOM