Electric is fixed, for $3,500.

The end of the neutral cable connecting the meter to the panel was gone at the meter end. All black (aluminum). Rainwater was flowing right on it probably since it was installed. Everything in its vicinity was replaced. I have all my lights on and nothing is flickering, for the first time ever.

My (gas) heaters got fried though. I'm hoping to not need to completely replace them, but the electronics are probably gone.

The problem was fixed quickly, thoroughly, and well. I'm not sure if I should have gone with a cheap quick fix and done more of the work myself. But at least now it's off my list.

Thanks very much to Dan Noé for correctly diagnosing the problem and convincing me of its severity, and mangosteen for convincing me to use Angie's List (once I gave up on the first electrician I tried).