Few weeks ago I fried my turnigy 9x by reversing the polarity.
How did I do that ? It's simple, I'm using a Li-Po battery pack and I plug it in the wrong side...
Now I will show you how I repaired my transmitter for about 1$ without P&P.

The reparation will depend of the damage on your transmitter.

Let's find all the fried components !

As gigi29290 experienced, components can be damaged without visual damaged (see comments). So if it's not working, try to replace all components described in this instructable.

Step 1: Find the Fried Component(s)

You'll have to disassemble the transmitter.
Then you'll have to find the fried components.
See pictures to see how it looks like.

One the first picture, you can see some reference.
On the second, there is my voltage regulator which is fried.
On the last one, there is an example of burned capacitor.

If your Voltage regulator is fried, go to the next step.
If it's the capacitor, go to the third step.

Step 2: The Voltage Regulator

The reference of this VR is 78L05 SOT-89.
SOT-89 is for SMD.
So if you don't have any 5V regulator, you can buy one here : http://fr.farnell.com/texas-instruments/ua78l05cpk/regulateur-20vin-5v-10-3sot89/dp/2112604
If you have another, regulator, check how to mount it.

The 5V output is on the left, the common mass is in the middle and the input on the right.

Now you have to unsolder it from the main board. It's not an easy part, personally, I had put my iron soldering on the three pins (bottom) and push it up with a cutter blade. You can also check the internet to see other method do unsolder SMD components.

Then, you have to solder the new one. Be careful with the temperature of your iron soldering, you don't have to burn or unsolder other components.

Finally, you can try to plug your battery.
If it work, congratulation !
If not try to see the third step to find another burnt component.

Step 3: The Capacitor

For this step, I only see this on internet.
My capacitor was not fried.

The reference is : 16V 22uF (SMD)

You can buy it on http://farnell.com
You can also buy/use an electrolytic capacitor with the same spec.

Now you have to unsolder the burned one.

To solder the new one, be careful with the polarity (see image).

You can now try to turn on your transmitter.

If it's don't work you can try to change other components.
Like the other 5V Voltage regulator next to the on/off switch (it's a 78L05 TO-92).
Or the other in the RF module (78M05 TO-220).
You can see this tutorial : http://openrcforums.com/wiki/index.php/Reverse_Polarity_Brick_-_Fix

Step 4: Conclusion

Now I hope your transmitter is working !

If you don't want to have this problem again, you can try to adapt the outlet to your battery pack, or try to add a polarity protection like this guy : http://diydrones.com/profiles/blogs/polarity-protection-for?xg_source=activity

I'm sorry for my bad English, and if there is some mistake don't hesitate to tell me !

Enjoy !