Hi Hawki - I had a similar issue about 18 momths ago. It turned out that the cylinder head in the GDi has a separate earth lead located at the back of the head held by a 8mm bolt. In my case the bolt was very slightly loose sufficiently so to have a poor earth. As the coil packs etc are mounted on the head over the spark plugs a good earth for the head is required.
In my case this was sufficiently poor to cause a 'turning over but no firing' situation exactly as you describe. Simply tightening the bolt cured it immediately. Awkward to get to though.
