If it's coming out from the output connection after you manage to stop the tap, it sounds more like a pressure issue (since it's only coming out of the output connection when the easier escape route - the faucet - is sealed off). I had an issue several months back after I dropped my nitrogen regulator - the next time I plugged it in, and set to the pressure I *thought* was 30 psi and opened the tap, it would not shut off. I had to tear off the body connect. I later discovered that the gauge was completely off, and was actually several dozen PSI higher than it was reporting (such that the regulator in the tap faucet could not stop the flow once it was opened).
Point being, it may be your regulator. How foamy is the beer coming out, and how quickly is it flowing? Other way to test is to try bleeding a little off the keg and seeing how hard/fast CO2 comes out of the keg.