Had the same issue, the pump does not prime on innitial start, this is normal, the problem for me was the coil packs, 2 of them wernt making proper contact with the spark plugs after i replaced the plugs and cleaned all the connectors the problem was sorted, the tops of the old blugs were melted where it was arcing... there is also a known fault with the coil packs with a green sticker on the top, the origional coil packs so check if you still have some of these...
Could very well be a relay issue for you as well... dosnt hurt to go through all the plugs, relays and fuses and give them all a clean