What engine do you have in your Sami - Suzuki never made a Sami with a 1.6, and although many Samis have had 1.6 engines swapped in, the most common swap is a Suzuki 1.6 from a Sidekick or Tracker and those are SOHC, not DOHC - they come in 8V with throttle body injection & 16V with port injection, and, depending on who did what when the engine was swapped, can be carbed or have one of several different EFI systems (1.3 TBI, 1.6 TBI. 1.6 MPI).
You have to figure out what yours has before we can help you.
By the way - none of the Suzuki EFI systems (that I've seen) had a cold start injector - there's enough injector capacity that they can increase the duty cycle to richen the mixture, most of them run the pump for a few seconds at key on to prime the system, and also whilst cranking.
Have you checked the fuel delivery pressure?