1st off, who still uses ZIP drives? lol those things were an epic fail
2nd see if the diskette is write-protected, there should be a little square hole on one of the corners with a plastic piece that slides over the hole, don't remember how it's supposed to be when it's locked, but try moving it to close the hole, and if it's closed alread, move it to open it, that may be the problem that's preventing you from copying stuff to it.

