It doesn't sound serious, if it's a button that "clicks". It sounds like the mechanism inside the button (usually a spring and metal arms or ball bearings) has broken. Although it's only the button, if the TV is old then it might be uneconomical to repair. If the TV is relatively new then you should seek a quote. Look for free quotes, don't pay someone just to look.
I'm not an expert but a similar thing happened to me. I messed about pressing the button until the TV stayed on and then just used the remote to turn it on and off.
LaurieP, February 2009
