I hope you are very mechanical-minded. Your machine is out of time, no more, no less..it happened when you broke the needle. Out of time means that the hook is not passing the needle eye at the proper time...all the cleaning in the world is not going to help...and truthfully, it also sounds as if there is not thread tension applied to the thread when the foot is down. so here is what you do:
1) Timing!: Remove the bobbin, throat plate, and this will give you access to all the hook, etc. There may be a port on the side of the machine that is rubber, and if so, remove it. Carefully mark the distance the hook is mounted on its shaft! Now, remove the hook by either loosening the set screw (probalby an allen screw) and check out the hook...if it has burrs, then use fine sand paper and smooth it out.
(the hook is the thing that goes round, then backs up, then round, then backs up when the sewing machine is turning...you will see the needle come down into the bobbin area. The hook MUST almost touch the needle and grab the thread going through the needle just as the needle starts back up! You time the machine by placing the hook back on its shaft to depth so that it does NOT actually touch the needle, but at the time the needle starts back up, the tip of the hook (it is the "sharp" part of the hook) just passes the needle...that will make the machines hook catch the needle thread, the thread goes into the hook's grove, the bobbin thread gets caught in the grove and twists the threads as the machine's needle leaves the fabric. Make sure there is bobbin tension on the bobbin case, and there is tension on the needle's thread (this is put into play when you lower the feed dog/sewing foot. When the hook is operating perfectly (you do all this by turning the machine by hand!) tighten the hook's set screw down on the shaft tightly.
2) Throat plate...It must be smooth, and if it isn't, sand it out to be smooth.
3) Upper tension" IF when you lower feed/pressure foot, there is no tension on thread and does not change tension regardless of the tension setting, you have a serious problem with the upper head of the machine. Remove or open the end of the machine where the needle is...check out to see why the thread tension is not releasing when the foot is lowered...there is some kind of obstruction OR it needs light oil...
All of this becomes very obvious when you open the machine...make sure then when you pull the bobbing thread when the bobbin is in its case, there is tension on the tread...too much bobbin tension will leave the sewing stitch with a straight line of bobbin thread on the BOTTOM of the fabric, too much upper tension will leave the needle thread a straight line on the top of the fabric with the needle thread...perfect balance of tension will make the "twist of thread" in the center of the fabric as you sew.
I hope this has been helpful. Goldwing