There are two cables. One that goes to the motherboard, one that goes to your power supply (or rather, comes from your power supply).
Some old SATA harddrives have the 4-pin molex for power (here’s a pic, for reference, of a 4-pin molex)
Most SATA harddrives have a different power connector though. It’s mostly flat. (here’s one of those, for reference)
If you look on your harddrive in a well-lit place, you should see clearly what you need. Unless your power supply is ancient, it will have at least 2 SATA power connectors.
although, if you only swapped your case, and no other hardware, that should not be an issue.