The hazard light button contains the relay for the turn signals as well. Do the flashers still work with the car off? If not, the relay inside may have seized up and you'll need a new switch. Pull the button out and whack it on something and you may get it to work again until you get a new one.

Not sure if this is a problem on the -40 series cars, but it's a common problem with the 850/-70 cars. The electrical contacts in the ignition switch begin to get loose, and sometimes jiggling the key will solve the problem of things not starting up. I doubt this is your issue though, as your headlights and everything else are working.