So I checked again and it does indeed have a 6-pin PCI Express connector. It was hiding behind something. So since I have a combined maximum of 25 Amps, it's presumably safe for me to install the Radeon 6670 without buying another PSU? What are the risks that it frys my whole computer?
Thanks again for the reply.
The Radeon HD 6670 is not a high power consumption card.
Your total system power consumption, including a Radeon HD 6670, should be well within that power supply's capability to power it.