How can I remove it a shiny coat on my dresser that was left behind by a clear plastic that i had put on it?

I own a wood dresser, so I decided to cover it with a plastic cover to protect it from scratches. After a couple of years I have decided to remove it. When I pulled it off I noticed that it had gotten stuck and after it was completely removed I discovered it had left a thick shiny coat that is a little sticky. any suggestions on how to remove this?How can I remove it a shiny coat on my dresser that was left behind by a clear plastic that i had put on it?
what about sand it down and refinish it? you could possibly use goo gone..but im not sure because its wood i would read the label...How can I remove it a shiny coat on my dresser that was left behind by a clear plastic that i had put on it?
Wood polish, Old English. DO NOT USE ANYTHING THAT WILL REMOVE THE TARNISH!