MY BOBBIN CASE HAS FALLEN APART AND I'M NOT SURE HOW TO PUT THE PIECES BACK TOGETHER.

Good that you included the photo...
The 2 pieces look like the hook and the retainer ring that hold the bobbin.
The piece to the left is the hook ... one to right the retainer ring. The bobbin fits into the hook.
There is a diagram below that should help.
The two black 3/4" long levers need to be twisted outward...then put the hook in ... followed by the retainer ring .... and then twist the two levers back.
Generally the two parts will only fit in a certian way to be able to successfully twist the levers back ... could be some trail and error
I tried posting another diagram but fixya would not upload it ... I will post this answer and then try to add the second diagram

Look for articles quoting hook, base and bobbin case. Youtube is excellent on things like this. There should be a clip either side to lock the piece in place.

I assume you actually mean the metal ring that holds the small round case that the bobbin itself sits in. There are usually two arms that swing in to hold that larger metal ring in place and then there is a plastic and metal piece that sit behind the large metal ring. fit the plastic piece that may look somewhat like a scoop next to the metal piece that usually has the post the the bobbin fits onto and has a quite sharp tooth on it. The metal ring then goes on to hold those two pieces in place and the two arms swing in to hold the metal ring into place. The bobbin or bobbin case now can be put back in. Hint on metal ring placement: they almost always have a notch that goes at the very top where the arm on the bobbin case sits in when it is in place. You may find it easiest to do this with the machine laying on its back so you don't have to have 4 hands to hold everything in place while putting everything back in.
Good luck!

looking straight on at the area where assembly goes, First clean and oil area, the jam was likely caused by accumulated dust or a small piece of thread . You should have three pieces, four including the bobbin itself. first piece to be replaced has a center post this piece goes into the machine by fitting it to the bobbin area, it will only go in one way so when it fits into place you will know. the next piece is a ring this piece has a small piece of metal attached to the top when looking at it correctly the two screws will be on top and there should be two indentions. first one is at 3 oclock and the other is at 9 oclock fit this piece into machine and there should be a lever on either side that turns around and rests in to indentions. replace your bobbin in the bobbin case ,be sure to thread the case correctly and load into newly assembled bobbin area making sure that it clicks into pplace

I don't think I have a picture but let me see if I can describe it to you.

The metal cutter has a black plastic piece. The blade fits in the black plastic with the longest point on top. The black plastic piece slides back onto the metal cutter, riding on the ridge. Fit the metal cutter back on the unit, being sure to align the "stubs" in the holes of the black pieces attached to the cog wheel. Make sure the "stub" of the black plastic piece with the blade fits in the parallel groove so that only the metal piece moves out and brings the thread to the blade when the cutter is activiated.

If you are still unable to fix, make a comment back and I'll go take pictures of my machine's cutter system.

Good luck.

I disassembled the top thread tension controller consisting of 12-13 pieces, including 2 springs. Since they all fell out on the table I spent about 2 hours learning the proper stacking order on the central shaft.
With a combination of reasoning based on each unique piece shape and trial and error I put it back together, adjusted top and bottom tensions according to the instruction booklet for the machine, tested some stitching, made final adjustments and all worked well.
I don't know what was changed in the process but it worked.
Don

That piece is a sweep that helps keep the hook clean. It is not necessary for the machine to use, I have thrown away many of them. If you can get your hook put back in you should be ready to go.
good luck!

Put the needle in the up position. Tilt the machine back with one hand and lay the hook in its position on what is called the hookrace. The little ledge inside the the circle opposite the other part that moves. Then take the outer ring and lay that in over top of it. There is a small pin on the bottom that fits into a notch. The two small nubs should be on the outside, then click the two black knobs over those. Put the bobbin in the case and the thread through the notch up under the tension spring on the case. Looking at the back of the case, pull the thread and in most machines the bobbin should turn clock-wise. Now snap it onto the post.
Your good to go.
Good luck.

There is one small metal piece 3/4 inch long and shaped like the letter "T" that fits under the right hand needle plate snap one screw. Attach to underneath square nut and can be seen sticking out from the top holding the bobbincase in place after the top plate is replaced and everything is back together. If this is not it, a picture would help as I have repair 100's of Elna 5000 to 9000's.
SewTech

This is for front loading bobbin..........

The Shuttle hook will look very much like this, and marries this to the "half moon" of the fixed shuttle.


The retaining collar ring that holds it all together has a plate like protrusion (like bull horns), this faces to the top and to the back.......there should be a small lug (or two) with corresponding small hole or slot on the fixed housing (hook race) that locates the ring tightly in the correct position.

There should be 2 swivel arms (black plastic at 4 o'clock & 8 o'clock)) that move to hold the whole thing together by clipping onto a small lug on each side of the ring.

If you tip the machine 30 degrees on its back while you do all this, it makes the process easier, as things are less likely to fall out.........support the back with a soft object for convenience (tissue box, pillow etc)

The bobbin case goes in after the housing is assembled, if you try to do it first, it will prove more difficult.

If this is not quite accurate for your model a photo of the bits would be helpful