Kenmore Sewing Machine Not Stitching?

I have a Sears Kenmore sewing machine model 385.1884180. It picks up the bobbin thread, but does not stich. I have gone by my model's booklet and have changed the needle twice with #15 to sew cotton. I have re-wound the bobbin 5-6 times and changed the bobbin. I have re-threaded the machine/needle, opened the bobbin section, cleaned it (sucked it out with vaccum cleaner) and oiled it. Still no stitching. Your help would be greatly appreciated. I need it to work properly. I do a lot of volunteering sewing. Thank you. No stitching at all. Sometimes a couple of stitches, then a big skip then a a stitch or two. Then nothing.