You're correct on the years of the two battles between the Spartans and Cougars - 1986 and 1987. I came up to both of them. '86 was Salem's first-ever playoff berth. The Spartans had beaten Pulaski County in week nine in a game that still rankles most PC Cougar fans to this day. I won't go into specifics, but that win down in Dublin, where in those days visiting teams never won, put Salem football on the map, IMHO. A rematch in the regional final was highly anticipated (mostly by the afore-mentioned PC fans), but Courtland crashed the party by beating Pulaski Co. 8-7 in the first round, by getting the winning safety when PC had a punt snap go out of the end zone with about thirty seconds to play. IIRC correctly, Salem won 21-7 in the '86 meeting with Courtland, and your Cougars prevailed 21-0 the following year. I recall that game being cold as blue blazes, and we Spartan faithful had absolutely nothing to cheer about all night. Then, we got in our vehicles and drove over three hours back home. Fun times.
The other year you're thinking of is 1989. That was the first time Salem went 10-0 in the regular season. The quarterback was sophomore Stephen Magenbauer, now the Spartans' head coach. He also played safety (or maybe linebacker?) on defense, and was a bonafide Division I prospect at both positions. Magenbauer was injured while playing defense in the first-round win over Dan River, when he lowered his head to put a hit on a Wildcat ball carrier. He was motionless on the field for quite some time, and to this day I have never heard a more deafening silence in Salem Stadium. Magenbauer was actually paralyzed for some length of time (hours, not days, but not sure of details), but eventually regained full feeling and use of all limbs. The injury had revealed a congenital spinal defect that had gone previously undetected. Of course, his days of playing contact sports were over. Without him, Salem managed to get past Brookville in the Region III final, but lost to Blacksburg in the state semis at the Stadium. Pouring salt in the wound was the fact that Salem had beaten Blacksburg in the regular season, though it had been close (9-7, perhaps?). The then-Indians won the rematch 26-14, and beat Courtland the next week for what to date is Blacksburg's last state title in football. Some of us Salem fans remember '89 as the first of "the snakebit years" from '89 to '92, when each season Salem was probably good enough to win state, but for various reasons, didn't.