I have a circuit with 4 recessed lights and a dimmable light switch. I replaced all 4 lights with dimmable CFLs and when I press the switch, they do not turn on. If I replace ONE of the lights with an incandescent bulb and press the switch, they all light up.

Why doesn't it work if all 4 are CFLs? Any ideas?

Dimmable CFLs are noted for poor reliability working with "standard" dimmers. See for example:
http://www.lutron.com/Education-Training/LCE/Pages/DimmingCFLsandLEDs.aspx

I don't know if changing the dimmer to a purpose built one for CFLs will solve the problem, but it's probably worth a shot.

So, if I read this correctly, you only change one fixture to incandescent, the others remain as CFL's, and all light up?