Muted 39110 hours

You get muted as a punishment for wrong behavior (insults, flaming, racism,..) after several reports from other players and with such a score (39110 hours = 4.5 years ?) you certainly know why it is there. There is no way to remove it if it is justified. Your account isn't lost, you can still play, only communication will be blocked.

If you don't know where this comes from you can try to contact support to know the reason or get it removed if it's a bug.

If this is your first time being muted, this is obviously a bug. It can happen for several reasons (issues when connecting to the server, when a patch hits the client sometimes mute times go crazy, etc.). I once got muted for a negative amount of time (something like -258 000 hours) even though I was not muted. Restarting the client got everything back to normal (maybe reinstalling the game can fix this, too).

If you really got muted for the first time, it should be 24 hours, so contact Valve support in order to know what's up. If it's not the first time then you should know why you are muted and at that point there is nothing much left that you can do. You'll still be able to play, however, you won't be able to chat: You can still use alt + click commands and the chat wheel to communicate.