If it's not locking back, and not picking up rounds, then it's short stroking. Here's a copy/paste of some of my AR troubleshooting notes, for reference for you and others.
It's a machine, so malfunctions are systematic. Only a few things can cause short stroking, failure to pick up, and failure to lock back (in no particular order):
1) Over length buffer bumper. Test: Can you pull the charging handle far enough to lock the bolt back by hand? If yes, then this is not it. If no, cut/sand the tail of the rubber bumper to give you sufficient clearance. The forward face of the bolt should draw approx 0.25" behind the bolt catch when fully rearward. If the bolt travel is gritty, exhibits any catches, or presents significant drag, there may be some other damage or dimensional interference between the BCG, buffer, and receiver extension - this should reveal itself in the buffer length test.
2) Out of Spec Magazine. In this case, the mag sits a little higher in the well than it should, so the top of the mag lips drag on the bottom of the bolt. Tests: try a different mag. You can also "paint" the top of the mag and/or bottom of the bolt with layout fluid (Dykem) or a magic marker then cycle the bolt on top of it, looking thereafter for witness marks. Another test: load one round, drop the mag, then fire while pushing on the tail of the bolt catch. If it cycles fully and locks back, you have a contact problem.
3) Insufficient bolt travel during cycle, typically due to improper gas system performance. This can be a loose gas key, poor gas ring seal, out of alignment gas block, plugged gas tube, undersized gas port, insufficient dwell time, under powered ammunition, and gas leaks in the system (block to barrel, block to tube, tube to key, key to carrier, and gas rings). Tests: Much of this can be checked by pulling the upper, removing the BCG, inserting an empty case into the chamber, and blowing into the muzzle to feel for resistance. Look for carbon blast marks around the block on the barrel, on the gas tube where it inserts into the block, and on top of the carrier where the key is seated. Also inspect the end of the gas tube and the mouth of the gas key for carbon build up or torching. Confirm the gas rings are in good shape, and confirm the gas key is tight to the carrier. Clean the gas system thoroughly, and try again. You can also plug the gas tube and try blowing again - you can't generate 15,000-25,000psi like your rounds will (rifle to carbine), but you may be able to identify a gas leak which hasn't left witness carbon - with the chamber and tube plugged, you shouldn't be able to blow through the muzzle. This is most likely your issue.
4) Insufficient mag follower travel. This can be caused by dirty mags, weak springs, warped/damaged mags, or under spec mag well. The mags aren't elevating rounds quickly enough to beat the bolt. Test: try a different mag. If a new mag works, clean the old one, check the spring and replace if necessary, or replace the whole mag. Really don't expect his is it for you - but it could be if your first few rounds run fine when the spring tension is at its highest, but then failures start happening. If you feel friction inserting the mags, you likely have mag bulge or an under sized mag well.
5) Excessive action drag. Similar to the out of spec mag problem above, if the bolt isn't traveling freely, it might fail to pick up. Usually this also presents itself by failing to close very frequently, as the rearward force in the cycle is much greater than the forward closing force. Tests: You should be able to feel excessive friction when cycling the action. Again, if you aren't getting failures to close, only short stroke failures, then friction is unlikely. A thorough cleaning and proper lubrication will solve this problem.