I hope you will share with us where you already have searched to help those of us who would enter the chase on your behalf. Always a helpful practice.
First, have you laid eyes on the original handwritten record? You may be able to distinguish initials or some other info that was not transcribed.
Have you looked at all the other soldiers on this muster roll? Anyone else from the islands?
Why not try the Daughters of the American Revolution web site? http://services.dar.org/public/dar_research/search/?Tab_ID=1
How about the Sons of the American Revolution applications, which are online at ancestry?
Have you queried Pennsylvania Archives?
Have you looked at the history of the regiment? Where are all the other soldiers from? Sometimes there are clues?
Who recruited him? Sometimes there will be records of where this man was active in recruitment?
Have you checked arriving passenger lists? He would have had to come into the colonies via some sort of port? Be sure to check Baltimore port lists as well as Philadelphia.
Did this man get a pension after the war? Have you checked NARA?
And, are you checking Marten as well as Martin?
Hope these are helpful compass points.
Laura in NC