Pekka
Magneto's - ON
I have experienced this in a C-172 with a carb.
What I did was I switched the magneto's OFF, pulled the mixture to Idle cut-off, opened the throttle half way and cranked the engine for a few revolutions.
After that, pick up the start checklist and start over again. It usually fired up but if your R44 doesn't you should check your magneto's as Whirlybird said.
In the C-172 you could also give a little fuel while cranking by milking the throttle but just a little. I am not sure if this is an ok procedure in the R44 though?
In you position I recommend that you recharge the battery and drink a lot of coffee while waiting.
It is great to see how fast people here react to this cry for help! Great work people.