Hello, my name is Rusty. The IEC cord (power cord) can get loose connections over time. IEC cords are famous for that. Plug the end in firmly where it meets the machine. You can use another cord if you have one around they house, they are universal. As they get older, dust can collect in them, or heat from the power can spread the contacts apart, preventing power from connecting.
You are right, there isn't a power switch on that unit. Concentrate on the power cord itself, and you should be able to get it going.
That fax was made before planned obsolescence was a thing, so you should still get years out of it, as long as it hasn't been dropped or mishandled.
Did you see any change by messing with the power cord?