Hello Mr. Tony,
ALL remotes will dim the lights on a paddle fan. (at least, out of 30 years of doing this, I've never seen one that didn't)
If you must have CFL's, you will need to purchase "dimmable" CFL's.
The button on the remote will either dim, or brighten the lights the longer you hold the button down.
Now, as far as them not working:
1) Replace the batteries in the remote (if you haven't already) If this doesn't solve your problem, then:
2) turn off the power
3) Inspect around the light fixture, itself and you should see two or three screws that attach the fixture to the fan's housing.
4) remove these screws and the fixture will come apart.
5) check the connections inside to see if either one of the two "Quik-conn's" are loose or have come apart completely. I have seen this happen on fans that have been in use for over 5 years.
If this inspection yields no reason as to why the lights don't work, get ready to remove the canopy above the fan. In this canopy, you will find the receiver. It may just need replacing. Next, check the connections up inside the junction box, as these also, could have come loose.
Let me know if I could be anymore help. Good luck in all you do and may God bless.
Electrician since 1977