I seem to remember that for some reason something horrible happens if you start the R44 with the throttle open at all. I can't remember why; and I think it's R44 specific, and I could easily be wrong. However, maybe check before taking ShyTorque's advice...though he normally knows loads more about helicopter flying than I do.
I haven't tried it in the R44, but in the R22, if you over-prime, leave it a minute, then put the mixture to lean, start, and when the engine fires, push the mixture to rich immediately. But don't worry, if you don't push the mixture to rich quickly enough and the engine stops, you'll have simply burned off the excess fuel, and you can now start as normal.
Done it quite a few times on the R22, and it ought to work the same on the R44.