The only problem with our new car? Well, see, they only had one key when we picked it up but hoped to find the other one. So we swang by Lowe's and had a duplicate made right away. The problem -- new keys? They have chips in them. So if someone tries to copy your key and steal your car, the car "knows" there's no chip and won't start.
So, now the car is fine. They still can't find the other key, but have promised to reimburse us for a second key, for which we have to go to a Honda dealership (bought our Honda from a Toyota dealer because they had a better deal on used cars).
I guess this also solves the mystery of the dashboard light that looks like a green key...