This "beauty" fires, ejects, and jambs feeding the next round, the round seems aligned but only gets 1/2 way into chamber
There is no troubleshooting manual for the MG34 (though I am tempted to put my notes together and publish one!)
This is often caused by one of several factors - let's go through the list.
1. Improper charging: 2 methods work for the TNW:
Method 1: lock the bolt back by pulling bolt all the way back, engaging safety lever, then EASING the bolt forward onto the safety (letting it fly can jam it against the safety). Then put a belt into the feed tray with an empty link over the belt. Close the top cover. If it doesn't latch, switch the position of the feed arm located under the top cover. Relieve the tension on the safety, disengage it, and let bolt go forward. There will be no round in the chamber yet. Then pull the bolt all the way back and let it fly forward. This should charge the gun and position the belt to feed properly on subsequent rounds.
Method 2: start with bolt forward on an empty chamber. Put the belt into the feed tray with an empty link over the bolt, and first live round in the next link to the left. Close top cover. Pull the bolt back and let fly. Then pull bolt back and let fly a second time - this will chamber the first round. Should cycle after that.
I would load 5 rounds max on the belt until the gun is stable. If it goes full auto, you may have to twist the belt to stop it. This is very rare on the TNW MG34 and is a malfunction.
2. Non-lubricated belts - lubricate the inside of each belt link with machine oil to allow the round to be stripped without losing all forward momentum of the bolt. German units often used paraffin wax for lubrication and to store loaded belts.
3. Loose flash hider: flash hider should be finder tight and one of the machined grooves should engage the "retainer hook". A loose flash hider inhibits recoil impulse and short-cycles the gun.
4. Booster cone - check for excessive carbon buildup on the booster cone assembly and on the ridges at the end of the barrel. Also, measure the diameter of the hole in the booster cone. TNW is notorious for using very tight cones that trap excess gas and put additional stress on the action during cycling. I like a 10 or 11mm cone, but have seen several 9mm diameter cones.
5. Misaligned top cover. If the gun has been charged properly and doesn't feed the second round, place a thin (0.5-1cm) piece of wood on top of the rear sight and push the top cover all the way up to rest on the wood. Then gently push the far end of the top cover down a few times using the wood as a fulcrum. This will bend the top cover hinge a tiny bit, making it more flush with with the feed tray. Manually cycle a few dummy rounds on a belt to confirm good cycling.
TNW has also recommended machining a wider slot for the round in the feed tray - I prefer not doing this - let's get the gun working as originally designed.
Please check these items and report back. Hope this helps!