Check if the machine is in the bobbin winding mode. To wind the bobbin, the bobbin spindle has to be moved to the right. (The hand wheel will not turn if the bobbin spindle is in this position.) If it is, move the spindle to the left.
If the hand wheel turns, then check for a thread jam. Remove the top thread and take out the bobbin case. Gently turn the hand wheel forward and backwards until the thread comes free of the hook in the bobbin race. Follow this by cleaning any lint from the bobbin race of the sewing machine.
The last possibility is that the belt has failed. This belt transfers the energy from the motor to the needle bar. One source of the belt is http://www.sewingpartsonline.com/motor-belt-singer-007158xxl5.aspx . You can find YouTube videos on changing the belt. There are other parts that transfer the forces form the belt to the needle bar. However, I suggest you find a good sewing machine mechanic if any of these parts fail.
The manual has good pictures of the bobbin spindle on page 11 (page 18 of the PDF). Singer has the manual on their support page: http://www.singerco.com/support/instruction-manuals
. The direct link to the manual is http://www.singerco.com/uploads/download/e06cb85928ace9753f1a7124f4a2df6168ffecf0.pdf
I hope this helps.