For all his foolishness, alexsanchez got me thinking about a question I'm hoping Jay or some of the other aerospace expert types here can answer.
Assume that Eagle had some kind of catastrophic computer/electronic failure. Would it be possible for a human being with Neil Armstrong's level of skill and training, assuming that the absolutely essential systems were still somewhat functional, to manually lift off and get into an orbit from which Collins could maneuver to a rendezvous?
On the face of it, it seems that you should. Eagle was sitting right on the equator (well, almost); it seems that if they could get the ascent engine to fire, if Armstrong could keep the spacecraft stable, all you really need to do is get enough altitude to make sure you clear the terrain, then - keeping your "back to the sun" - pitch over and gain about, what, 1500 m/s or so of tangential velocity to get into some kind of orbit.
Collins had spent endless hours working on "alternate rendezvous" scenarios, trying to work out all the possible ways to go after the LM if they were unable to rendezvous as planned. If they could get into almost any kind of orbit high enough for him to reach them he probably could have. Even if they couldn't get the ascent stage into a stable enough attitude for him to dock with it, they still had the "space walk" option to get back into the CM.
Maybe it would have been impossible - I don't know, that's why I'm asking. But despite the stranded-on-the-moon scenario, I just can't picture Aldrin or Armstrong sitting down and waiting to die while there was anything at all they could reroute, hot-wire, or bang on with a hammer.