Why is the water supply for my refrigerator not turning on?
When you first turned the valve on, did you hear any movement of water at all? If so, the problem lies in the fridge (to get any further help here, give us the model #). If not, there is an upstream valve somewhere, or the plumbing is disconnected. If you're unsure, you could always disconnect the fridge, and open the valve a tiny bit to ensure water does come out of the line (obviously be careful not to spray water everywhere). 

If the lines goes down through the floor, and you can see underneath the kitchen floor, you should be able to trace the line back and find any valves. If it is going through the cupboards, then it probably connects under the kitchen sink. 

If it's going into a finished space, then you'll have to do some guessing. Hopefully no one was dumb enough to hide a valve behind drywall, and certainly not in the 'off' position, but it's always a possibility. 

See if you can find the same size tubing anywhere, probably wherever the closest plumbing to the fridge is. Not much else uses the 1/4" or 3/8" flexible tubing typically used. From an unfinished area, you also might be able to see between the joists into the space above the finished area, and this might help you locate pipes as well. If you can't fit your head in, a camera (possibly with a flashlight instead of the built-in flash) can be very handy for getting a peek. 



Fridge supply lines often connect with saddle valves. These are terrible little valves that usually fail after being used a few times, but at usually fail in the 'on' position (or in otherwords, leak). 



Since you already have a valve behind the fridge, it's probably not a big deal (eg, the saddle valve can be kept in the 'on' position), but if you do end up having to ever deal with it (or you have a plumber in anyway) you might want to replace it with a T and proper compression valve. 


  Aside, I didn't notice till after I posted it, but in that random picture of a saddle valve I found, it looks like there is another saddle valves above, probably failed, with a crimped copper tube coming out of it (maybe in a sad attempt to seal it?). Perfect illustration of why not to use saddle valves. Pretty sure the one in the middle is just a ground wire connection.




Keep an eye out for any other (closed) valves as well, as it's possible there's a bigger line running to the fridge before it changes to the smaller tubing. Likewise, keep an eye out for disconnected tubing, as it's possible someone ran this line but never actually connected it.

If you still can't find it, the next thing is to call in someone experienced (eg, a plumber), and if you REALLY can't find it, cut open the ceiling below the fridge and start tracing that way. Depending on your skill levels and how destructive you're willing to be (aka, how much you're willing/able to repair) you will have to decide how far to go before calling a pro.

Good luck!