The ZIP drive was working before but I tugged on the power cable and messed it up. I tried fixing it with that red and black one but no luck. I tried plugging the cable in every way possible; which might be responsible for it not working in the first place
Yes, quite possibly blew something in the drive by sending 12VDC into something you shouldn't, or maybe 5VDC into a ground line.
I saw your last picture illustrating the original power cable where the molex connector is separated from the wiring and wonder if you may have slipped the wiring in the wrong molex slots (4 slots) when attempting to fix it. And when you plugged it in, instead of applying 5V you may inadvertently applied 12V.
Simon may be right (more so) . . . you may have exceeded the zip drive's required voltage. A multi-meter for taking voltage and resistance (for performing continuity tests) would have been handy to identify voltages at mainboard power connection pins. Taking readings is an absolute must before connecting a power cable at mainboard so you know what pins are "live" and how much voltage . But you must know and have an understanding of electricity. If not then you must seek professional support from a qualified tech.
Peace.