The Marlin model 80 (no letters) was made 1934-1939. These were excellent hunting or plinking rifles- darned accurate- not to a bench rest match standard- but pretty darned good. You also did OK on the price. More than OK.
No serial number, huh? I could do the "Send it to me and I'll dispose of it for ya" routine, but I have too many 22s now. Half of mine also have no serial number. That is because they were not required by law on rifles and shotguns until 1968. Never had one, never needed one, perfectly legal. Mine go in my record books as NSN- No Serial Number.