the hose is your postive crankcase ventilation... its no big deal... just make sure isnt totally open for too long... so the car is correctly turning over? if it is then the battery isnt at fault... when you pulled the coil did you make sure that it was still grounded when you checked for the spark? they ground through the engine which they need to spark... when you pull the spark plug is there a smell of fuel in the cylinder or is it smell dry?
ps. whats the picture for? im trying to connect the numbers for some project but cant think of one??