Even if your coin were to look like in the picture, Blake, it would remain slightly collectible. These old Danish coppers are pretty scarce today, and even tainted examples regularly sell for small sums at Internet auctions.
Frederik VI was King of Denmark from 1808 until 1839, and also king of Norway from 1808 to 1814. During this latter period, Danish coins were minted for circulation in Norway as well.
The values listed below are catalog values, but also take into account the actual prices of recent successful auctions. You will, as always, need to refer to our Important Terminology page found at the top left in order to properly interpret these catalog values.
worn (as in our image): $8 US dollars approximate catalog value
average circulated: $24
well preserved: $45
fully uncirculated: $80
It is safe to say that a fully uncirculated specimen of these coins with great eye-appeal potentially could sell at a professional auction for more than $80.
Severely damaged coins that are bent, holed, corroded or have other significant problems will be practically worthless to most collectors.