What sort of welding was done? If it was gas (oxy/acetlyene) there's no cause/effect relationship.
For electric welding, there are different trains of thought on this - old school stick (arc) welders will always tell you to disconnect the battery before doing any welding, but the younger generation using wire feed welders may disagree - personally (and I'm not a welder, I'm more of an electronics person), I'll disconnect the battery - takes just a minute or two and I like to play it safe.
I know some of the US market Samurais had a feed back carburettor with an ECU, but I don't think the SideKicks used it - I believe those were either TBI (throttle body injection) on the 8V or MPI (multi port injection) on the 16V - so don't take anything I say as gospel.
Can you see fuel spraying from the throttle body when you crank it? Try pouring a cap full of fuel down the throttle body and see if it'll fire.