Hard to diagnose without feeling the shifter. It sounds like the shifter is not allowing full engagement of the gear. That said, if it is correctly adjusted then it's gearbox rebuild. Sounds like the PO sold it just in time. Sorry.
Good - Fast - Cheap: Pick any two.
E23 735i; E30 318i; E32 735iL; E38 735iL; R50 Cooper; R55 Cooper Clubman.
E21 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i