I have a Pfaff that was all gummed up like that. I kept oiling over the whole winter and finally got it free. You may need to try Kroil and see if that helps. The stuff I got came in an air can so I sprayed some of it in a can then brushed it on. If you do use it and it frees up you will need to use some oil on the machine after that. Triflow will work but it could take a longer time. I have seen Kenmore machines freeze up like that from oil. There is no sacred place for it to not accumulate. The buttons, needle, the bobbin area, everywhere that moves will have to be degummed in order for that machine to work. Turn the machine in every direction after you oil. In other words oil then turn on its side. Next time oil and turn it on its other side. Next time oil and stand it on end. Upside down you get the idea. That oil has to run in. Then you might have to do it all over again. The Pfaff was not only gummed up it had a needle tip stuck somewhere. Once it got slicked up and the needle tip out it is a good machine. Hopefully no one tampered with the zig zag timing but that is fixable as long as it isn't a bunch of plastic.
That said I have a Kenmore still runs in reverse because I can't seem to find some tiny little gummed up place inside that machine. I have traced and traced but I can't seem to nail it. I may need to dig it out and put it under the bench in rotating positions with drops of periodic oil for a winter some time, too.