Where can I find replacement knobs for the dual slider lutron fan light switches?

You need to run another (separate) wire from the ceiling fan/light to the wall box, so you can wire one slider to the light, and one to the fan.

Call Lutron's tech support center directly at 1-800-523-9466. They're available 24/7 andif you're just looking for a knob or part of the knob, they'll probably just send it to you.

I don't think you can do what you are trying. The fan & light are on one circuit. Probably, originally, there was only a light fixture there. The fan/light is on a single circuit and the remote does the controlling of both units.
Now, you are trying to install a fan control and light dimmer but you don't have wiring for each separately.
You might be able to use one of the dimmer controls to adjust the output to the fan/light combination, but you can't control them individually, if I understand your wiring.
Gary

As a general rule, grounding will not affect operation of dimmer.
Type of dimmer, type of switch being replaced, type of load, and how you connect wires will affect dimmer.

Here is Lutron dimmer switch page
http://www.lutron.com/Products/StandAloneControls/Dimmers-Switches/Pages/DimmersSwitches.aspx

What is the load? Are you wiring dimmer to a ballast? Or fan? Or incandescent lights? Or florescent lights?
Are you replacing a 2-way or 3-way switch?
What color are your dimmer wires?
How many wires were connected to switch?
Can you re-install the switch, and know where each wire went?
Did you replace a light with a fan, and then want the dimmer to slow the fan? Not every dimmer will work with a fan, or florescent lights.
Dimmers cannot dim LED lights.

If I know what type switch you are replacing, and the type of load you want to control, and the specific dimmer you have, I can answer the question.

http://www.google.com/products/catalog?q=Dual+Fan+Control&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a&um=1&ie=UTF-8&cid=13402817922409280930&ei=_PCyTK64KcSAlAf6rPzkDw&sa=X&oi=product_catalog_result&ct=result&resnum=6&ved=0CD8Q8wIwBQ#

The link above goes to google products and lists several sellers

Lutron S2-LFSQ is made to control one ceiling paddle fan & 1 light. Switch will not work on florescent lights.
See manual

To use this product, your fan and light must already be controlled by 2 separate switches.

If you have just one switch that turns on the light & fan together, the S2-LFSQ will not work (without additional wiring).

Okay, you have two switches. One switch turns fan on-and-off. The other switch turns light on-and-off.

Here is wiring diagram from manual: See diagram larger



Here's how to wire:
-Before disconnecting wires from existing switches, mark each wire with tape and pen.
-There is one wire that feeds power to both switches > mark this the 'Hot wire' and it connects to Lutron black wire (if you are unsure about this wire, remove switches, separate wires, turn on power and test each wire to bare ground, tape tester leads to wood sticks so hands are away from power, Tester lights up on Hot wire)
-The switch that controls fan > mark this the 'Fan wire' and it will connect to Lutron Yellow wire
-the switch that controls light > mark this the 'light wire' and it will connect to Lutron Red wire
-Lutron Green wire or bare wire connects to bare ground wire.

Unfortunately, there really isn't a whole lot you can do here to fix it, any attempt you make to strengthen the grip on the slider may gum up something else in the process. Usually they test for this sort of thing before it leaves the factory so I'm actually quite surprised. The best suggestion I can offer is to call their technical support line (they're available 24/7) and they will probably replace the unit for you.

I believe their is another part missing when it fell apart. But it is better if you replace it with a new one.

sorry i don't have what you need but i know that dimmers and fans never work well they always buzz from the lack of power you will actually burn out the brushes in the fan in a short time.

I have searched high and low for this. Can't find it. if you find one please let me know...
What I have done in th past is separate the fan and dimming with two devices and if you're in a multi gang box you can combine other switches into a combination unit, or add a side-car box onto the one you already have in the wall...