My iMac won't recognize USB keyboard

I've been using a USB keyboard ever since the one that came with the Mac broke and recently I've been having trouble every time I turn my computer on.

The Mac doesn't seem to recognize the keyboard at all, and I have to keep changing the chord between the four USB outlets on the computer until it finally works, sometimes it takes over half an hour before I can get it going.

This happens every single time, before I can type my password to log in. I've tried the keyboard on a different computer and it works fine.

Any help would be deeply appreciated!