OK, the K&N you showed, isnt the problem one..
If bike starts, when jump started, the your battery is suspect. Measure the voltage while cranking, if below 10 volts the battery is no good. Bike starting when warm indicates the battery has charged up while running, but the cold start problem indicates that capacity is lost after sitting overnight..
Its a relatively cheap starting point, to replace the battery.
Most STs will drop the headlight when starting, but there seem to be a few that dont.