While I don't have this particular machine -
Most of these universal motors use electronic speed controls that use a device called either a TRIAC or SCR, that regulate the motor speed by chopping the mains frequency (i.e. turning on and off rapidly 100 or 120 times per second). The usual failure mode is a short circuit, which will produce the symptoms of "only runs at full speed".
These electronic speed controls also use a filter with capacitors and inductors, and it is possible that a shorted filter capacitor will also produce the same fault, as mentioned in another answer. The capacitors used are known as "X2 class safety capacitors"; they have an internal mechanism that is supposed to clear faults by blowing internal fuses, however this mechanism may not work with low current loads (like sewing machine motors).