Sounds like you may have chat blocks on? Check them on the wrench menu.
Also you can't see global messages when the tab is set to "Chat" as shown in the picture. You have to have it on "all" or "global chat" (The little bar at the bottom) "Chat" is strictly for isolating the local in-game chat. Global is separate.
If you get muted a little message shows up in the bottom left of the screen every time you log-in that lets you know how long the mute is for. It also gives you a "you're muted" message any time you try to send a message. Your messages are in the chat screen so you're not muted.