The LA Rams made a trade in 1986 that may have finally gotten the LA Rams a quarterback.
No it was not the Jim Everrett trade later than year. It was a draft day trade with their arch rival, the SF 49ers.
The LA Rams traded to 49ers:
QB, Jeff Kemp
1986 4th round pick #96 Charles Haley
1986 4th round pick #101 Steve Wallace.
49ers to LA Rams
1986 4th round pick. Which should have been pick #66. But the NFL took 20 minutes to make the deal official. Jeff Kemp was unsigned. At that time in the NFL, you couldn't trade unsigned players. So the NFL took 20 minutes to correctly "word" the trade, the LA Rams actually traded "the rights" to Jeff Kemp.
If the LA Rams were able to keep pick #66 the would have taken QB Bubby Brister, but since teams are suppose to make their selections within 5 minutes, the LA Rams pick became pick #71 and they choosed QB Hugh Millen.
Of course in hindsight, if the LA Rams had drafted Charles Haley and Steve Wallace, they would have gotten a pass rushing LB and an All Pro RT. Both Millen and Brister had journeyman careers in the NFL.
The above information from an Sports Illustrated story.