I built my first AR and I'm pretty proud of doing it.  Was much easier than I expected.  However, I took it to the range and had a big problem.  It won't cycle.  I shoots fine, but it's basically a single shot and have to manually pull the charging handle back every time.  A couple of issues is that it has a carbine gas system but a regular buffer and spring.  Also, each round seemed to stick in the chamber.  I literally had to pull the handle as hard as I could and bang it on my thigh to get the bolt to come back.  The thing shot beautifully (nice tight 1" group at 20 yards).  

When I got home I noticed the gas block had come loose.  I fixed that and also bought a new carbine spring and buffer...but I'm still concerned that the spent casings seemed to get stuck in the chamber.  I mean that bolt was not moving without serious force.  Could that be because instead of the casing being ejected, it was sticking in the chamber due to expansion?  

I hope to be able to get back to the range this weekend with the adjusted gas block and new buffer and spring...but if that doesn't fix it what could be the problem?

What ammo?
What kit did you buy?

I'm confused.............By "regular buffer and spring" do you mean a rifle buffer, rifle spring, and rifle receiver extension? If so, you can't just go slapping a carbine buffer and spring in a rifle receiver extension. You will have to change the receiver extension to a carbine tube.

Until you clarify your buffer/spring/receiver extension set up, I can offer no further help.

+1 to the above.  

It does sound like there is a bur or you have a rough chamber. Pull the barrel and give the chamber a good look.

As others have stated more information about your ammo, barrel, gas system, buffer, receiver extension (buffer tube) will help diagnose your issue.

If you have a stainless barrel steal ammo will often stick in the chamber.  Same with any barrel if the chamber is tight. Try brass ammo or hone the chamber a bit larger.
I have had to enlarge the chamber on a couple barrels to get them to cycle steal ammo reliably. I have never had brass cased ammo stick though.

Well, the obviously loose gas block wasn't helping, but that still shouldn't have made the case stick.  Your chamber likely has some debris or tool marks.  Could be a "tight" chamber if it's a match barrel.  

Buy a nylon chamber brush and a cheap-ass walmart rifle cleaning kit.  
Take a section of rod from the cleaning kit and attach the brush; chuck up the other end of the rod in your drill. (A variable speed drill is the way to go if you have one).  

Take the upper off your rifle.  Run the chamber brush in and out while spinning in the drill.  Don't go crazy, 10 or 15 seconds is plenty.  
Then, take a live round and drop it in the chamber, it should fall in easily and completely with a nice thunk.  Tilt the barrel towards the ceiling and the round should drop right out.  (or fall out with a light bump)
If the round sticks or drags going in or hangs up from dropping out, go back to the chamber brush.  
This shouldn't take more than a few tries.  If it does, there's likely something else going on.  But without more info that's all I got at this point.  

If the above doesn't work -

What is the make, model, and chambering (.223, 5.56, Wylde) of your barrel?  Did you clean and lube the barrel first?  
What type(s)s of ammo were you using? Brand?  .223 or 5.56?  Brass or steel case?  
A picture of the inside of the receiver focusing on the barrel extension and feed ramps would be helpful, as would a picture of the chamber lit with a flashlight.

Buffer tube is definitely part of the problem. After reading a second time, I'm starting to wonder if the OP bought a 223 barrel and chambered it in 556 at the range

Stop throwing parts at it.  Figure out what is wrong first.

Hook a piece of tubing onto the gas tube and try to blow through it.  Is there something preventing gas from moving through?  Is your gas block blocked?  

Chamber a few rounds.  Don't fire it.  Just get a feel for how it functions when you're not dealing with the firing cycle.  Does the bolt stick?  Or is the casing actually sticking in the chamber when you fire it?  

What barrel do you have on it?  What ammo are you using?

Definitely a 5.56 barrel.  Stamped right on it.  It's a BCA 16" 1:8.  The ammo was American Eagle 55 grain FMJ.  The bolt is an Anderson Nitride.  The Upper is Aero.  The stock is a Rogers Super Stock (not sure what tube goes with that).

It's a 5.56, but I bought the lower kit first then the upper kit about a month later.  At the time I bought the lower I wanted a rifle length gas system so I got the appropriate spring and buffer.  When i went to pick up the upper kit I changed my mind to a shorter hand guard and carbine gas system.  So I had carbine gas with rifle buffer/spring.  Got the new spring and buffer installed today and it is a much lighter pull for sure.  I also really lubed up the bolt...a lot more than I used to in the military.  It could be that the parts weren't properly oiled being brand new.  I'm hoping to get back to the range tomorrow to try it out.

It does not matter what lower buffer parts you have compared to the upper. What matters is having all the correct parts in the lower.

The stuck case sound  like a gas problem, the proof is your loose gas block. Fix the gas block issue first and make the ports are lined up.

Sounds like the bolt carrier group BCG starts to move back then jams the fired case back into the chamber because it did not move back enough to eject the fired case

you can use a rifle buffer and  spring with a rifle stock only, the gas system has nothing to do with it.  for a stock like you have, the carbine stock/collapsible type, you must use a carbine buffer/spring.  the gas block being loose  needs addressed and likely was part of the problem...

Should I put loc-tight or something on the gas block screws?

Sounds like my gun guy sold me the wrong spring.

its not just the spring, the buffers are different.  if you put a rifle buffer/spring into a carbine stock, there wont be enough reward travel for it to work properly... that's why you had to jam it open.  here is a picture of the difference.

Sorry man, I didn't mean to question your intelligence about the 5.56, but you never know lol. This sounds like a gas system/buffer issue to me. You said you bought a full sized buffer/spring originally, so I would try putting that in and seeing what happens. If that does nothing, check your gas system and make sure everything is on right and in the right place. If that doesn't work, it's got to be something with your bolt carrier group. I would check it out thoroughly and make sure everything fits and is put together properly. Check the extractor, make sure the butt of a round fits well inside the bolt. Check the chamber too and make sure there's nothing funny going on in there. It doesn't happen often, but it's possible that one of your parts just happened to be a lemon. Good luck!

Based on that picture, I had the carbine buffer to start with but a full length spring.  The new spring is Several coils shorter.

I'm a big dummy...gas tube installed upside down.

Fixed it and now it shoots like a champ!

that's great, but you had another problem.  is that fixed too?

the carbine spring worked perfectly.  I was hitting 1" groups at 25 yards (indoor range).  Worked flawlessly once I got the tube right side up.

You can and I do. However, being that the gas block gets hot, it will melt the loctite and from what I understand, deeming it pretty much useless.

I use red loctite for my screws.

Thanks.  I'll give it a try.

Red Loctite melts at high temps too. Flexbar Rocksett is a 'thread locker" that is unaffected by heat but still can be removed with hand tools.