You're reffering to how Aldrin broke the ascent engine arming breaker and they fixed it by using a pen to throw the switch? It was possible to bypass the switch, but they didn't need to because the pen fix worked. It wouldn't have really changed anything. The LEM was a great machine like that.
If they can't fix it or bypass it for some bizarre (almost ASB) reason, and they can't take off, they die. Their bodies remain on the lunar surface unless NASA retrieves them with another mission. Mike Collins flies home alone, Nixon gives his prepared speech. Given the highly public failures of both major spacecraft, public support for NASA may wane, and the American lunar program may end even more prematurely than OTL.