So what I gather from your question is that you have a two prong plug which has no common (green wire) and only a hot (white wire) and negative (black wire). You can wire a three prong plug with the existing cord, you just will not have a common (green wire) connection. wire accordingly : white to silver terminal and black to copper terminal and ignore the terminal with the green screw.
"Ye can lead a man up to the university, but ye can't make him think."
Finley Peter Dunne