No letters in front of the number? Could be my list is for older machines.
I have two OLD singers right now. A 1913 Model 66 and a 1937 model 128. I needed to buy new wiring for the 66. The 128 was missing the plug. I got both on Amazon!
You can look up age and model using the serial number. Here:
https://ismacs.net/singer_sewing_machine_company/serial-numbers/singer-sewing-machine-serial-number-database.htmlBe careful you differentiate between 6 and 7 digit numbers.
Oh, and your machine may simply need oiling. Once you know which one you have you can look up an owner's manual.
What is amazing to me is that some people are able to get machines that have been used as lawn ornaments and doorstops in barns going again. They'll seize up from rust but they'll soak them in oil and or Evapo Rust and clean them up.