These vital files are on a Power Macintosh G3 (about 20 years old) which has no usb PORT.  I've tried to connect the two with an ethernet cross-over cable, with no success. Then I realized this old mac has an internal zip drive with the 100 MB disk still inside! So now I'm able to copy the files, 100 MB at a time, ONTO this zip disk. Any ideas on how I can get them from the zip disk onto a usb flash drive or onto my imac?Not without another ZIP drive, USB or IDE.  The one in the Mac could be IDE or SCSI.  If it's IDE, you can remove and connect it to the DESKTOP PC, if it has an IDE port on the motherboard, some newer motherboards don't have it anymore.
The Mac G3 has USB ports, but don't know if they will recognize USB flash drives.  Here's the G3 specs:  http://support.apple.com/kb/SP133Are you able to connect to the internet with your G3? Probably with a 56k modem? If you can (it will be slow) then could you not transfer your files to a free data STORAGE site (password protected) and then access them with the other computer. truenorthCheck your area for data storage/recovery services and call for pricing on moving the data over to another media...