I'd suspect neutral safety switch alignment due to worn shifter bushings. You don't state whether column or floor shift, but in either case, try holding the shifter all the way in Park with one hand while turning the key with the other.
I have worn bushings inside the column and have to hold in Park probably 80% of the time. A handy anti-theft device most of the time.
'73 280SEL 4.5 (9/72)- RIP
Only 8,173 units built from 5/71 thru 11/72
'02 CLK320 Cabriolet - wifey's mid-life crisis
2012 VW Jetta Sportwagon TDI...at least its a diesel
Non illegitemae carborundum.