Rain hitting down pipes

I had a similar problem and added a length of corrugated tubing to my existing downspouts.

What was happening is that the water came down the downspouts too close to the house. It did not have time to soak into the ground and pooled around the foundation. So using some black corrugated pipe and the right adapters got that water 5-10 feet from the house.

It is very low cost, just get some of the black pipe, the right adapters to attach to your downspouts, and sheet metal screws.

Throwing the main breaker on your electric panel is easy; you should try that. If cutting the power to the whole house stops the problem, then turn the power back on and start turning off circuits one-by-one. Hopefully they're labeled so you can identify the appliance or room, but this may take some trial-and-error.

Here are some other possibilities I can think of:

• Pump for well water (if you have it).
• Some other vibration coming in via municipal water line (although I can't imagine what would cause repetitive vibrations from a water main). If you do get water from your city/town, try to find the main service entrance and put your hand on it, to see if the pipe is vibrating.
• An exhaust fan: maybe in your attic?
• Radon mitigation fan (these typically run 24/7, drawing air out of your basement/crawlspace, through a duct).