How do I repair my Singer 5511 when the bobbin won't wind?

SOURCE: singer quantum 9420

give this site a look
http://www.singerco.com/resources/operation_basics.html

SOURCE: Bobbin won't wind Singer 7422

Your problem lies with the main shaft that is to tight to release the bobbin winder mechanism, because of old grease and oil becoming sticky. A short term solution will be to remove the needle, in order not to hurt you, and then hold on to the needle bar with your left hand, while engaging the bobbin lever with your left hand. This will prevent the main shaft to rotate and your winder should work. In the long term, take it to your dealer to clean the oil and grease. You will not be able to open the machine casing yourselve, as you might damage the casing and or electronics.

Good luck!

SOURCE: Bobbin is not winding correctly

slide plate may be worn - i had the same problem. try holding down the center of the bobbin with a pin while slide plate is in the winding position.

SOURCE: Singer Sewing Machine model 9224. Bobbin thread

If you turn the handwheel, can you see a metal ring rotating around the outer edge of the bobbin case? If not rotating, broken gear or timing belt off.
If that ring is turning, remove the needle plate and bobbin case. As this ring now rotates, you will a finger on the ring that will pass behind the needle from right to left and it should catch the thread from the eye of the needle. If this finger, the "hook" passes above the eye, you have a timing problem.

Let me know.

SOURCE: I have a singer 503A. The bobbin winder will not

When you have the winder rubber on try and turn the winder by hand, if it does not move the chances are the winder has seized, if the winder wheel is moving but not the spindle then the grip (thread) has worn, if you cannot move the whole winder by hand and it has seized you need to get some WD40 and spray a few drops down the spindle, take an electric drill and put it over the top of the spindle and switch it on slowly and it will probably free it off, be aware of oil splashing out.
you mighjt get a digram from www.tandtrepair.com