The vehicle is backfiring through the exhaust and won't rev up.

Hi,I dont know if this is a timing belt or timing chain,
but if it is the belt drive timing belt then its possible that it has slipped a couple of teeth so that when it fires on a serton cylinder when one of the exurst valves is still open cousing it to back fire through the exurst,
I would first set up the engine timing,make shore that the mark on the crank pully is lined up with the pointer thats on the engine block then make shore that the cams are both lined up with the marks on the head,if ok,then you can adjust the ignition timing,
you will already have it at top dead centre by sorting out the engine timing,so take the distributer cap off the rotor should be pointing at the number 1 cylinder so it should just be ready to fire,if that seems to be lined up ok,its not your timing.
so you will have to do a engine compression test to see if there is eneything wrong with the valves or piston rings(most of the time its the problem with the head)if thats ok,then it must be to do with a fuel problem if you have a good spark from sparkplugs.
all the best,hope this got the brain cells working hard so you can get to the bottom of the problem.

Back firing indicates a number of things but usually an over advanced timing system. Have you had the timing checked?