HD 6870 with 1.3 HDMI Cable

I just bought a new 6870, a Benq G2222HDH monitor and a 1.3 HDMI cable. The monitor gets no signal. I've tried with my TV and got the same result. I know it's not the card because I've connected it to another monitor and it worked, although it was a different cable (unfortunately I don't know which one; it came with a Gateway FHX2300). Are 1.3 cables not compatible with 1.4a ports?