Computer problems?

A common problem with Honda is their Immobilizer Sensor that goes around the Ignition Lock Cylinder and it picks up a special code from the key that allows the car to run. Have all your codes checked especially your Immobilizer System. This will not able to be done by a Parts Store, you need a shop that has a good enough scanner to check the Immobilizer Codes. Have all the Computer Systems checked, you will find your problem then, for sure.

It's almost certainly the ignition switch. Honda had a recall for it for 8 Accord but the replacement one is the same as the original so has the same defect so may have to be changed every few years.