Is the lever coming up all the way to the lower tang when chambering a round? Marlins have a built-in safety that requires the lever be all the way up before it will fire. This is so it will not operate before the cartridge is fully chambered.
Try a different ammo to see if you get the same results. Also check the chamber to make sure nothing is keeping the round from chambering.
Are you using reloads? Did you trim the cases to the proper length before loading them?