What they said. There are only a few things that can kill power to everything. But first you must look for that clicking thing. In 99% of the times on our trucks that click is the Ford starter relay/solenoid up on the fender. But if something was added to yours, such as a circuit-breaker, you'll need to know about it.
If you did the install on your A/C however, I'm guessing you know your way around the engine compartment already, and would have noticed something odd like that.
So for the regular culprits, these come to mind first.
1. A bad battery cable. Not the starter one, though that can get old too. We're talking about either the positive or negative battery cable here. So far this is the most common reason we've run across here I'd say.
2. Loose or corroded battery cables. Check both ends for clean and tight. Happens often enough to need being one of the first things you should check.
3. A failing battery. Not common, but can happen.
4. A partially burned through fusible link. I'd say this is low on the list of suspects, but since it's not impossible it's good to verify yours is still good. You can see them when they get puffy and almost melted looking. If yours appears this way, replace it.
5. The big connector in the large black wire at the back of the ammeter. If this connector comes lose, or has gotten rusty over the years, it can create intermittent power failures. If this one goes out, you lose power to everything. Same as a battery cable.
if it's a battery cable this would not surprise me. It would be one of those cases though, where it's likely just a "coincidental failure) that had little to nothing to do with your A/C install.
And old or compromised battery cable can look fine and still be bad. But if one or more were borderline anyway, perhaps all the disconnecting and reconnecting and bumping in to while installing the air-conditioning could have sent it over the edge.
Good luck.
paul