Well, not literally every electrical connection, but definitely the battery leads, distributor and ignition coil.
I focused on the plug wires because they seemed to be the one component that when touched or otherwise manipulated would cause the car to immediately start.
The logic I am applying stems from childhood: when my electric trains were running crappy, or not at all, I cleaned the metal tracks and locomotive wheels of all dirt and oxidation. After that, they were good as new. Because I cannot remember the last time I cleaned my distributor and spark plug wire contact points, their potential condition or cleanliness causes me to focus so hard on them. That plus the fact that the wires were draped over the side of the engine in such an unnatural manner, and after restoring them to their proper place, all was (almost) right again.
I am also surprised at how easily the ignition coil wire came off. The end on the distributor requires considerable effort to remove. The end on the coil slid right off, indicating a rather loose connection.
Also, I went through a period of months when my engine bay was being drenched (literally) by leaking power steering fluid. It is reasonable to assume that some oil and dirt seeped into key electrical contact areas. I'll know for sure when I remove them later on.