First make sure that your keyboard is proprerly connected to your PC.
If your keyboard is connected, you may be using incorrect syntax in the game. Try speaking to your immediate area using the /say command. For example, type:
/say can anyone hear me? This will display, Can anyone hear me? , to the players in your immediate area.
Another thing you should check is to make sure you are in the correct filtered chat area. If you have the Group tab up you may miss out on other chat messages. Be sure to view the Main tab when testing chat functions.