There are numerous threads on this site that tell you how to clean and lubricate a 401 (or 501). The machines were close to the last really good sewing machines made by Singer. However, they are 60 or so years old at this point. In that 60 years, the old oil and grease has dried up, especially on those machines that have not been used. That old grease becomes like glue after all this time.
The 401 was built to really close tolerances, so that "glue" keeps the machine from moving quietly and quickly (or at all) like it should. You just have to clean, oil, clean, oil and clean and oil again. It's not hard, just time consuming.
I love 401s, so would definitely not suggest you part it out. If you part it out, you will still have to clean it and de-grease the parts. You can probably get more for the machine in working order than from the parts. Not much breaks on a 401, so I wouldn't think the demand is really high.
Here's the thread from when
I worked on my first 401. There are numerous links in this thread. They almost all lead to expert help.
Good luck.
bkay