Where can one buy old 737 parts?
Airliner parts have a tiny market outside of the airline and maintenance businesses (in the sense thst the general public generates no demand) which means that there probably aren't many places to shop for unairworthy (read: cheap) spares.  I would place "want to buy" ads on Barnstormers and maybe cruise the site from time to time clicking through relevent categories.  I did see one ad offering 737-200 parts but you'll have to contact the seller to see exactly what they have and how much they want.

You could certainly buy a new part but you will not like the price tag.  I imagine that an unairworthy spare for an -800 series will be hard to find compared to a -200, for example, because of the quantity of inoperative junk parts generated thus far by the respective fleets.

Good luck!