I was ready to say the starter until the steering wheel comment. That could just be a fluke though. I'm no mech by no means but I have had 2 cars with starter problems and what you describe (aside from the sterring wheel) is everything I went through. Have you tried the screwdriver trick when it doesnt start?
if you're talking about jumping the solenoid with a screwdriver, then your problem ain't the starter. At least not on a Ford where the solenoid is almost never located on the starter. Rather it is under the hood, usually bolted to the inside of the fender rail.
no you're not mistaken. the starter shuts off with anti-theft so jumping it wouldnt help. i was thinking it may be your starter when i first read it though Im not a certified gm mechanic just yet.
OK guys...slow down and lets start simple. All this PATS and solenoid stuff is further down the line once we determine it isn't the battery or the alternator. The steering wheel was probably just at a weird angle at lock is all in your other post. Bad PATS wouldn't allow a jump. As short or bad key switch wouldn't allow any power therefore no "click" The solinoid on the newer cars is attached to the starter. At least it is on my 96 Mustang, 03 Expedition and 06 F150. But we will wait for the outcome of the batt and alt check to go further.
done. 1st step as always is to check all connections. Especially since jumping it off works. I'm assuming he's already done that much. a battery won't be so dead as to offer up only a click, then 20 minutes later have enough juice to start a car without doing something to it. No battery will charge itself that much just sitting there. Let alone go through that process (being dead as a doornail, then magically charged a half hour later) multiple times over the last few months. That eliminates the battery as the main culprit. highly unlikely it's the altenator as well, because the battery has pretty much proven not to be dead. only way for battery not to be dead, is if the altenator is putting out like its supposed to.
LSUfan71 is right. If the car always starts when jumped, the problem almost has to be battery or battery cable/connection related. Clean the connections and try that. It is possible that the battery has an internal problem, that could create an open circuit, rare but not unheard of. Keep in mind that any movement or current flow can close the open circuit or bad connection as well as open it, thus the intermittent problems. Good luck, and be careful, if the battery is faulty it could blow-up. Not a good thing.