I removed the UPS - tower power wire, and instead plugged in the power wire from the tower to the wall socket.
So basically now I've got:
UPS to wall socket.
Tower to wall socket.
Which obviously makes no sense. However, like I said, when I tried this setup:
UPS to tower.
UPS to wall socket.
It did not work. I only have one space for a power wire on my tower.
What to do? Thanks!