Why won’t my car crank if the battery is charged, and when the ignition is off it makes a weird humming noise.

 

Are we talking about a 1983 Accord? Or at least some kind of Honda?

Generally, if the battery is charged, then you can check the battery cable connections, then maybe the starter motor.

 

2004 Honda Accord

 

4-cyl or V-6?

Just so I don't take anything for granted, lack of cranking means the starter motor is not spinning the engine, right? Does is make any heavy clicking noise in the engine bay?

Try hitting the starter with a broomstick or something while someone holds the key in the START position. If that "caveman test" causes it to start that means the starter is the problem. I don't remember if it's reasonable to rebuild the starter for that year, or just replace it.

Does the humming sound come from under the car near the rear axle? That's the EVAP system venting occasionally which is normal.