It is not unheard of, hell, it's not uncommon, for a fine Beerenauslese level Riesling from a decent year to hold up for 20 years.
If you don't know, Beerenauslese is a term which indicates not only grape ripeness (sugar content) at harvest, but harvest method. For beerenauslese wines, the ripest grapes are individually picked.
Unfortunately, 1984 is generally thought of as a poor year in Germany, and we can use germany as a guide (most critics weren't paying much attention to aAustria back then).
I also don't know if your wine is Riesling or some lesser varietal.
I saw this wine sell for 10 British pounds about three years ago - that is not a good(high) price, so that is not a good sign.
The color could be acceptable but murky is not a good sign.
Still and all, buy some dessert wine you like, chill them both and pull the cork. If it is no good, you can drink the wine you bought.