Both the clutch switch and the ignition are good leads.
I've had the ignition problem and I don't think it prevented me from starting the car but rather wouldn't allow me to turn the key or take the key out of the ignition. Your video shows that the ignition switch is sending power, at least to the instrument panel...my guess is other things like the radio work as well??
I had a Nissan Pickup w/manual transmission and the clutch switch went on it twice. I think in both instances the problem presented intermittently, (e.g. sometimes the truck would start and sometimes not) and after a time, in both instances it stopped starting altogether. I remember when it happened the second time I was at a gas station and I got stuck at the pump and had to have the truck towed to the dealer.
The symptoms you describe may be more related to this clutch swith issue..but it's just a guess.
The clutch switch repair cost was about $100 or so for the Nissan...my guess is it won't be that much for the Cobalt.
Let us know what it was.
2010 Cobalt XFE
2006 Chevy Colorado 4x4
2005 Toyota Corolla
2013 Kubota M5640 SUD
Last edited by keegs; 12-07-2011 at 11:18 AM.