Yukon/Tahoe Starter Problem

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

I had intermittent start problem with a 1997 Tahoe. Bad relay in the fuse box.

Put a voltmeter on the starter solenoid, small wire. If it doesn't get 12V when turning key then problem is upstream, relay or ignition switch. If bad relay you can test by swapping out a similair relay from a non-essential circuit, like A/C.

If solenoid gets 12V signal you should hear the solenoid engage (one click). Then check the voltage on the larger solenoid terminal connected to battery. This is to make sure you've got good connection at terminal-cable-battery and plenty of juice.

In your case IF you really hear the solenoid click THEN it's likely the solenoid. There's a copper button on the other side of the large terminal that gets pitted after extensive use. In that case get rebuilt starter.