I have the same problem, but eventually I could solve it. Turning on and off iMessage or Facetime never works unless you find out the root cause. Follow the following steps:
1- First is to make sure your settings for iMessage and Facetime is correct
- Your phone number is correct in "My number" (Settings>Phone). Double check it in your iTunes
- Time zone is correct (Settings>General>Date & Time).
- Regional format is your country (Settings>General>International)
- Wifi is on for Facetime; Wifi or 3G is on for iMessage
2- If you cannot activate iMessage or Facetime after doing the above settings, 99% the root cause is your SIM. Micro SIM of iphone is very sensitive, I mean, if the SIM does not fit the tray completely, it will cause activation error to such functions as iMessage or Facetime even though calling and receiving functions are still work normally. What you need to do is simply change your SIM (it costs less than one dollar in my country) or check the fitness of your SIM on the tray. Power off and on your iphone and activate iMessage and Facetime. It takes about one minute for a successful activation.
If you doubt of it (your SIM is the cause), borrow your friend's SIM and test it on your iphone