The chances to recover your coins are small since those exchanges probably no longer exist. I hope you can learn from this and store your assets on your own wallet if you plan to hold for long term.
Op didn't said his coin is lost in an exchange, he is only stating to know exactly what's happening on those old coin trading on those old exchange, along the way, those old exchange was hacked like cryptopia, coinexchange, etherdelta, forkdelta, all of these collapse along the way.
If you want to know the surviving ones you can quickly look at the first 10 coins on the coinmarketcap, check if the coin you bought is there an do a thorough research if they are still doing well in the space.