Many Hondas of this era are under a Recall for faulty ignition switches and this can cause problems such as the one your car is having.
A quick look shows yours is under a switch Recall but not for that reason. This has more to do with the interlock than an electrical breakdown.
However, just because your car is not under a Recall for failed switch contacts does not mean the switch is fine. Many non-covered cars suffer the same problems as the covered ones but politics being what it is, the car makers often succeed in keeping the damage to a minimum as far as numbers go.
Just something for consideration anyway.