DHT11 Humidity/Temperature Sensor Interface with PIC18F4620
The DHT11 sensor you are using appears to use a protocol similar to 1-wire, though the timings look a bit different at a glance. This was invented by Dallas (now Maxim) and is used in many of their devices, the DS18S20 is an example of a similar temperature sensor to the DHT11 made by them.  

My experience with 1-wire (and the above maxim part) is that is a great protocol but can be a little fiddly setting up on a small micro due to the quite fast and not-so-tolerant timing, especially if you are using a lowish speed oscillator and C. However this 1-wire part seems to have more relaxed timings and data direction appears to be only one way, so things should be a bit simpler (although the maxim part can do more)    

Anyway, the initial presence detect for your part is an easy one since you just have to hold the line down for at least 18ms, raise it high for 20-40us and then release it (set to high impedance input)
I'm not sure why it says to pull it high for the 20-40us, when releasing it and having the pullup do this (the Maxim parts do it this way, and this is standard for open drain communication) would have the same effect and prevent any potential bus conflicts, but it may be to do with the rise time needed. In any case as long as you release the line before 40us it should be okay.  

I haven't checked everything, but in your start signal code it looks like you are doing things correctly (although I would avoid setting the output low before setting the pin to input) so it's likely it's to do with the micro settings or a connection issue (e.g. miswired pin, open circuit)  

A few things to check:


Have you tried a simple blink LED routine to confirm your LED is setup correctly?
Are you absolutely sure your delay routines are producing the correct delay? Have you confirmed this on a scope?  
Have you confirmed the PIC pin is actually outputting the high/low levels correctly to the DHT11? (i.e. pin is setup and connected correctly - test at DHT11 pin to make sure signal is reaching it)   
Is the 5k&Omega; pullup resistor (recommended in the datasheet for lines &lt;20m, if longer you may have to reduce the value) present on the line?