I have tried 3 times to replace the pull chain switch on my ceiling fan and I now only get it to work on high speed. My question is if I leave it on high speed, can I hook up a switch at the wall to control both the fan & lights separately? The fan is wired with black, white & red wires, but at the switch I am only seeing black & red wires, with a white wire connected together. If I have 3 wires at the ceiling, would that always mean you have 3 wires at the wall? What type of switch would you recommend for my situation? Thanks for any advice you have!

You do have 3 wires at the wall, the red, black and white. Odds are great you have the wrong switch, exact can be tough, some same numbers have been know to have different switching.
You can have the red and black at the wall go to 2 switches.
You are lucky you have High, just leave the switch alone, use a Fan control for speed.
You could even add a transmitter and receiver for remote control.

Thanks for your answer, it is helpful! The only thing is I'm finding most of the wall switches are wired for 2 wires, I would need one that has 3 correct? I want to be able to control the light & fan separately, but with one switch. I think I've seen one switch with dual control. I was going to try the Lutron "Maestro" (fan/light control), but I see the wall switch only uses 2 wires and it uses a canopy module at the ceiling... not sure if this is right for my wiring since I have 3 wires? Thanks for your help!

These are good:
SLIDE COMBO FAN 2.5A CONTROL - LIGHT 300W DIMMER- WHITE | eBay (http://cgi.ebay.com/SLIDE-COMBO-FAN-2-5A-CONTROL-LIGHT-300W-DIMMER-WHITE-/270583049814?pt=LH_DefaultDomain_0&hash=item3f0001ae56)
And look through these:
http://shop.ebay.com/i.html?_from=R40&_trksid=m570&_nkw=slide+fan+light+control

Examples were shown, go with a good company, try to avoid the real cheap?
Hard to tell where some are from.

First, for the pullchain issue, what make is the fan?

Ceiling fan pullchain replacement and repair - Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-pullchain-replacement-and-repair.php)

Blades won't turn. Motor hums and lights do work. Doesn't appear that the shaft is turning

See if blades spin freely and direction switch is NOT in the middle position.