You didn't say which version of FTM the file was created in. Usually GEDCOM is only needed if you are going to change genealogy programs. Current versions of FTM do a good job of working with older vesion files.
Go to your local Genealogy Society or Family History Center with the file on USB or CD. I'm betting someone will know a member who would be willing to fire up their copy of FTM and convert it for you.
Another option is to install FTM on your new computer and just copy the file to that computer by what ever is the easiest method.