Low idle and sporatic engine kill

My vehicle has been idling rough and sometimes killing at stop lights and has been doing so for about a year. I've had the throttle body cleaned as well as the fuel injection system but the problem continues, I'm now being told that a compression check shows that #3 cylinder has 130 and the others about 200 and that I have a burned exhaust valve which is causing the problem but I'm having a hard time with accepting that and the check engine light hasn't come on, could that be the problem??