This machine is 22 years old. It fell off the table after our German Shephard climbed onto the table. The outer casing is'nt cracked or damaged, the power comes on, but the machine only works in reverse gear. My questions are: (1) What may be the problem? (2) what will it cost to repair this?

if you had the needle plate in position at the time , it probably fell onto the table or the floor
to check remove the plate and check around the bobbin carrier and shaft
get another one from any machine repair shop

If you can, pick up your machine, turn it upside down and shake it. Be sure to put down a towel or something on the table because those little screws will roll or bounce to unimaginable places! If it doesn't fall out, you may find it rolling around inside the case where the bobbin is located.

you need to oil the machine and perform maintenance on it,did you oil it??,did you read your manual and figure out what preventative maintenance you need to do?? Customer Support

You will note the round shape of the spring is some what raised on one side. Insert the spring so that the spring is raised in the Center. ... Toward you ...then be sure to insert the small clips in the outer edge of bobbin case. Also rotationally be sure the flat portion of spring is configured in the same position as the shape of the opening of the bobbin case It's purpose is to put pressure on the bobbin and control back lashing or spinning of bobbin

What does the left over piece look like?

You can get a manual here - http://gotoes.org/sales/ConsewSewingMachineManuals/ViewInfo.pl?Consew=1&Sewing_Machine_Model=1118-3

You may be able to (very carefully) super glue the pin back on where it broke off.

Thank you very much for showing an interest in my problem. To begin with - I don't have a Singer machine - I have an Empisal 666 automatic and it was the timing to a great extent. All started with having given it for a service (nothing was wrong except I was lazy to do the job myself!) and during that service the guy, mechanic (for want of a more appropriate word!) had damaged the plate under the foot where the feed dog sits, it was cracked, which caused the thread to come up through the feed dog instead of in the centre as it should, and the cracked and bent plate (approx. 3mm) was putting pressure on the feed dog mechanism causing a timing problem. He had also smashed the spring on the bobbin case which gave the tension problems. So it cost me the price of a bobbin case (AUD$9.00) and a lot of swearing!! Managed to straighten the plate in the vice and all is working as well as can be expected.
I should mention, to find out all this, I had to take the machine off it's table and turn it upside down and only then saw the cracked plate. Have been sewing for 55 years and have always done my own oiling and cleaning etc, never had problems until this happened!
However, it would be very helpful if I could get a formula for fixing the timing in this machine. If you can help me with that would be great as I still need to fine tune that part yet, and I won't trust another repair man with the job. That's an excellent sewing machine.
Thank you very much for trying to help, appreciate it very much. Regards, Peggy.

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.

Your hook/needle timing is off and it needs to be seen by a technician before you damage the hook. Some dealers can do a 24 hour repair for an additional charge.
sewman7