The wiring could be bad. My 1948 American made 15-91 needs rewiring from the motor to the plug. It was in storage for many years in Texas, so the plastic covering on the wires appears to be partially melted. Look for places where the bare wires are showing. My Canadian 15-91 has the original wiring and is still in good condition. I coudln't find the serial number in Singers' databases, either.
It's unlikely the motor is bad. What would make the motor go bad is extensive use. Use wears down the "innards" of the motor. The parts are not expensive, but the labor might be. Your decals are still pristine, so it's unlikely that the machine has seen a lot of use. (On well used machines, the decals are usually worn in the front where you push the fabric through.)
It's also unlikely that it is out of time. Most of these old black machines are idiot proof. If they are not rusty, they will almost always work.
The wire to the wall and the wire to the foot pedal are connected. So, it would be unusual to have the pedal and not the wall plug. However, it would save money if you have the original pedal/controller. Here's what the original would look like.
lLINK Non-original replacements are less expensive.
Good luck.
bkay