I think the 1983 date of liability means it made it onto the new computer system, which I think was done sometime in 1983. Also, that is the date it last ran out of tax too, and it's well before the SORN requirement date, so yes it may still exist, but it's quite unlikely I think. I've been trying to trace the whereabouts of my old MK1 Granada Coupe, reg HCO437N, but that hasn't been taxed since I sold it in 1994 to a "MK1 Granada specialist", who I now believe was a banger racer. :cry:
The DVLA website may be slightly misleading as the date of liability I think refers to the last time the car ceased to be legally taxed, or SORNed, so if that date is before SORN was introduced on 31st Jan 1998, it could be that it is sitting in a garage somewhere, as it doesn't need to be SORNed if its been off the road since before that date. But it could equally mean that it has been scrapped.
With my Ford Anglia, which was last on the road in 1979
, we had a letter from the DVLA in 1983 saying that we had to inform them in writing if we wanted to keep the car registered on the new DVLA computer, (which we did), and that still exists, but has a date of liability sometime in 1979. So in reality, probably only the owner knows if it still exists.