That's not an ignorant question at all. Long maybe, but not ignorant.There are several aspects to it.
Your picture of how gas molecules exert pressure just by bouncing off the walls of a container is quite good. The energy exchange isn't really relevant. What counts is that on each bounce the particle gives some momentum to the wall, as the particle's own momentum changes direction.
Let's take another aspect: why when you start with a liquid or solid in a snug container and then expand the container do some molecules fly off making some gas phase? There are several ways to see this.
One is that, unless things were cooled to absolute zero temperature, things were still rattling around in (for example) the liquid. The distinction you draw between vibrations and velocities isn't so sharp. Anything vibrating has some velocity, alternating directions.
If there's some space open, occasionally a molecule will get enough energy to break loose and fly off into that space. So those loose molecules are the gas. To totally "dampen out those velocities" means to cool all the way to T=0 K. You can't ever quite do that, and it gets hard to even approach it too closely. So your picture of the condensed phases as lacking motion isn't very accurate.
Under extreme pressure, or even under moderate cooling, you can largely suppress the vibrational energy, for quantum mechanical reasons. (For technical types, I mean you can get the temperature below the Debye temperature, so that the energies fall far below equipartition values.) Nonetheless, so long as there's some thermal energy present (and there always is), a few molecules will fly off into the gas phase, if they're given room.
A more abstract way of seeing the same thing is to start with the deepest principle of thermal physics- that nature explores all the accessible states over time. (That's a sort of informal way of stating the second law of thermodynamics, that total entropy gets maximized.) Failure to form the gas would mean that lots of states were staying unoccupied for no particular reason.
(published on 12/28/11)