Only a few things will do this:

battery (yes, you can loose just cold cranking amps, and still have power to the accessories),

loose or corroded connector on the battery,

starter (but you should hear a click from the general area of the starter if this were the case, and you didn't mention a click)

neutral safety switch (the car has to know that it is in park or neutral, or the signal will not be sent to the starter). If your shifter is loose, this is suspect, just wiggle it a bit, and try neutral instead of park.

Chris