My 2000 Mitsubishi montero sport lx is not firing what could be the problem?

for future reference alternators have nothing to do with your car firing or not ,,, all they do is put juice back into your battery,, and same with your starter and battery but all they do is turn the engine over,, so if its turning over its not going to be any of those things

now to start on your problem have you verified that your getting spark and fuel both ?

yez