enter your CD key on steam, I dont think the physical disk contains anything really anyway.
So, they give the user MULTIPLE discs that contain nothing?
As for the actual OP, if you're able to just download the game, log into R* Social Club and redeem it from there.
If I recall, the physical edition only connects to R* Social Club, and not Steam. Sign in, click the gear, game downloads, use rockstar code.
Or, at the end of the day, a new DVD drive is like $20. And that's for a good one.