Back when I was in high school a friend of mine formulated the rule of Levitt: If you are forced to solve a problem and you don't know what you are doing replace the cheapest thing first in your experiments. Did you disassemble it and clean and lube it when you first got it? It could just be gummy from disuse. Try swapping out the op rod spring. If you can't borrow a good one then clean and stretch the one you have a tad. If you haven't taken it apart already you may even find the spring is in pieces. Anyhow the spring is what operates the gun during the load cycle. Its hard to tell from your post if its failing to pick up a round and closes on an empty chamber or it fails to chamber a round it has picked up. Also with the spring out reassemble the mechanism and the wood and see if the loading cycle is hanging up on something by operating gently it by hand. Put the spring back in before firing it.
Also, try this: M-1 Garand tips accuracy improvements - Detroit Firearms | Examiner.com