would it crank?
if it cranked, however would not start, could be any of the following:
vapor lock
debris in carburetor
stuck or mis-adjusted choke
bad safety switch (operator presence switch)
bad ignition module
fouled cap and rotor
the next time it dies, pull off the spark arrestor and have someone give it two pumps of the throttle. you should see two streams of fuel spraying in the carburetor.
when you say its hard to start when its cold. specifically go thru your list as to how you start it.
you should be doing the following:
turn blower on
wait 2-3 minutes for blower to clear bilge of any vapors
two to three full pumps of throttle (sets choke and primes motor)
control in neutral press throttle only button at base of control, and bring throttle forward about half way
crank engine
when engine fires, pull throttle back to about 1200 - 1500 RPM
let motor run at 1200-1500 RPM for a few minutes while you remove bow and dock lines
pull control back to neutral (to re-engage shift function)
put in gear and go boating