I have a new alto sax, but it won't play notes below a low G.?

I'd make a suggestion to check that none of your holes have been stuck to the saxophone, so that when you press down they don't open. This is a common problem with beginner saxophones. The problem may also lie with your octave vent, which is the little part on the back of your saxophone a bit further up from the octave key. The part is meant to open and close the vent on your command with the octave key, in order to change the octave. It has some padding on it that may have deteriorated. If this is the problem, I got mine fixed for roughly £35, not sure what that is in USD sorry. Finally, this could just be a problem with your embouchure, you are new to the instrument and you do have to have a different mouth shape from playing the clarinet! Hope this helps!

This is how I started out; however, there was a problem with the saxophone and my old band director actually was not able to play below a low C. I recommend that you first get it fixed and then loosen your embouchure when you go down to low notes. Also, take a little bit more mouthpiece, and that can help when producing good tone. Make sure you have good posture, and focus your air to get the center of the pitch. Good luck!