Timing so rarely gets off..... Yet timing is blamed for everything. Some of those Singers have a belt around the bobbin area and some have plastic gears. Those should be checked. Your hook should now be checked for burrs since the needle was hitting it until it broke. Check your manual for correct needle insertion. Check inside your needle clamp for lint and other gunk. Check for lint in the bobbin area. It may be a good idea to have the machine fully serviced.