Are you absolutely sure the right kind of needle and the right kind of bobbin are in the machine? Especially with plastic bobbins, it is very easy to put one in that "looks" correct but is for a different machine. Also, are you sure that the thread is coming off the bobbin in the correct direction (clockwise or counter-clockwise, depending on the machine)? As a first step, I would try changing the bobbin so thread comes off in the opposite direction and see what happens.
You may need to clean between the tension discs on top using *unwaxed* dental floss. Any lint in there will cause the tension to remain static no matter how you adjust the knob.
I'm thinking that if the feed dogs move when you run the machine, the problem is most likely to be in the tension. Since you've already cleaned the bobbin area, I'm thinking it is the top tension.