How would I connect an internal 3.5 Floppy disk drive to a motherboard that doesn't have a ribbon cable connector?

Use an external USB floppy drive.

If you MUST have internal.... if you're good and creative you -might- be able to disassemble an external USB floppy drive and mount it like an internal drive.

Alternatively, you could hunt down an old LS-120 "superdisk" drive. Its an IDE drive (40 pin connector, like your hdd or cdrom) that reads floppies (in addition to high-capacity proprietary disks)