Remote control possibley defective

Simply use regular bulbs. It sounds like it is switched electronically probably via a dimmer. If the CFL lamps are not specifically labeled dimmable they won't work. I have seen the LED lights work where the CFL lamps will not. If you want to use CFL then replace the dimmer.

There may be another remote control in the room/house that is causing it to turn on. A member of my family has a fan that uses a remote, when they turn on their stereo it also activated the dimmer on their ceiling fan light.

step 1 would be to ensure that it isnt other remotes that are causing this to happen.

step 2 would be to replace the batteries in the remote for the fan. once they are replaced use the remote to turn on and off the functions that are being turned on randomly.

if it is not anything to do with remotes, have the person that put it in for you disconnect it from power completely to try to reset the control board.

if that doesnt help, you may have a defective product that needs to be replaced.

if this doesnt work, report back with some more detail and I will try to help.

If neither the fan nor the light work, check that there is power to the fan unit first. If it is remote controlled and there is power to the unit, any relays would be on a PC board inside the fan and will not easily be replaced.

Your remote control I would assume includes a dimmer for the light. CFL bulbs are not compatible with dimmers. If it has a dimmer, you must use incandescent bulbs.

Does the fan/light fitting have manual switches, pullcords?

If so, are you sure the manual switch for the light is in the 'on' position? The remote will not override the manual switch, so it must be on.

Apologies if you have already thought of this.

Hold the glass shade with both hands on opposites sides and GENTLY turn it counterclockwise. You should have access to the bulb.

At the top of the pull chain there is a metal piece; this is threaded on a bolt. Unscrew the metal piece and lower the globe to expose the bulbs then remove and replace the bulb(s). I recommend flourescents as they are more economical, run cooler and last linger than incandescents (regular bulbs).

Compact fluorescent bulbs do not work on dimmers.  You have to use standard incandescent bulbs or not dim the lights.

probably not defective bulbs. Flourescents use either a starter and transformer or a ballast. When lights are weak, could be either. Very simple to change too. One other thing, could be connections that go into the lamp holders. If not good connections, light will be dim. On a stretch, if unit is located in an area that us lower than about 50 degrees, this could cause them to be dim. Check ratings on ballast/ starter and transformer. Finally, if voltage is either too high or too low, this could be a dimming problem too. If it has worked in the past, and this is a current problem, then chances are it's not the voltage but may want to check it anyway to eliminate that possibility.

If you press and hold the light button, it will step up in brightness to max then back down to dark. Then when you press the button briefly it will turn off and then press button briefly again it will turn on at the intensity you had it at last. So if you are one tick from off you may not notice it is "on" because it is dark. A second possibility is that you replaced the bulbs with a compact flourescent and they are not always happy with adjustable brightness, often they will be on or off, no middle ground. I recommend sticking with old school bulbs in the fan.