Can a broken brake light switch....

.... cause the car not to start???

Hi there, new to the forum. Not an expert on electrical guys, here's the story:

I have a 2002 Ford Explorer Sport. My wife wanted to start it yesterday to no avail. It made a rapid clicking noise underneath the dash in the brake pedal area. So I thought: OK, must be a switch or relay. The engine did not crank at all. Here's the quick version:

- turning the ignition, key in position 1: at first it did the normal safety belt "ring" a little faint though, clicking noise from the brake pedal area, dash lights were on
- turning the ignition, key in position 2: no starter activity, no engine cranking, clicking noise from the brake pedal area, dash lights were on
- key in position 0/no key: the clicking noise was still there....clicking away
- unhooked the battery to save it
- checked all fuses (under the hood and interior fuse box left dash): OK
- did some research on forums => looks like the brake light switch is broken. Easy $15 part.
- Got a new brake light switch from autozone
- Installed the new switch, turned the key, one louder click => nothing worked at all, no dash lights, no starter activity, no cranking. Seemed like a completely dead battery or a blown fuse.
- Checked battery voltage (it's rather new anyway). Battery is fine.
- Checked all fuses again, all fine
- Though the new switch might be faulty, switched back to the old one. Turn the key, car starts, all perfectly fine. Hhmmmmm......

So with that I thought: no blown fuses, old switch might not be perfect b/c old, battery works fine. Must be something with the wiring. A short, loose plug/switch.

I just do not understand the cause/effect of brake light switch <=> engine not starting/cranking.

- Thought the new switch would be better than the old one and wanted to test it again. Installed new switch => car starts, all fine.

- Then my wife drove the Explorer to the store, got back to the car. Car wouldn't start.

- I drive to the store, unhook the battery, mess around with the switch (basically just taking it off of the pedal) Start the car. All fine.

- This morning I went outside if there are any issues with the tail lights. The car stared w/o any problems. All tail lights/signals work properly.

So I tried to diagnose as much as possible. As I said, not an expert on wiring/electrical, but since there is an issue to get the car running as well I think there must be a loose switch or plug, or a broken wire. Is the wiring harness that carries the brake light switch also responsible or the ignition?

Any help would be awesome guys. Another thing, I bought the car used in 2007, except from a new ignition coil I didn't have any serious issues with the car. I replaced the multi-function switch (turn signals, whiper etc.) in 2009 or so.

Thank you!!!