For the most part a Sidekick and a Tracker can be considered as the same vehicle with a different badge, but, we still don't know what engine you have because both vehicles used several different engines over the years, from a 1.6 four cylinder up to a V6, so the first order of the day is to figure that out and tell us. The most common swap is the 1.6 four cylinder, and there were two of those, and 8v and a 16v - if you have the 16v it'll say so on the timing belt cover. 16v engines have an alloy cam cover with the plugs in holes through the cam cover, 8v engines generally have a black pressed steel cam cover and the plugs are on the side of the head near the exhaust manifold.
Second thing you need to do is to figure out what was done with the fuel system during the swap - all the Sidekicks & Trackers came with fuel injection, 8v had single point or throttle body injection, 16v had multi-point injection - reading between the lines I suspect you may have a carburettor - if that is correct, then we literally have no clue what you're dealing with.
I get the impression that you acquired the vehicle after the swap was done, is this correct?
Fuel or fuel pressure is a distinct possibility, especially if the tank vent lines have been plugged - have you tried opening the gas cap when it starts acting up?