The fuse is good and the connection at the rear window appears to be connected. The light on the dash controls comes on but the ice or snow doesn't melt at all.
So, is the supply getting to the terminal on the window? If not then the cable can be broken in the area of the hinge...
Is there a ground connection? same issue with broken cable.
The third possibility is that all the thin elements have been damaged if the two things above are ok. One way to check is to use a test lamp or multimeter and check to see if there is voltage present on the small filaments.
(FWIW: Just my experience on an '04 Cavalier with the same symptom. Below is from my (scant) notes for that car, and AllData info on a '07 Cobalt.)
Per the AllData Cobalt schematic, the defog circuit shows TWO 'relays'. The first  is in the Body Control Module, which is "... Below the radio, on the right side of the center console". If the dash light is coming on, this 'relay' is working.
This control circuit then goes to the under-hood fuse block, where there is a second relay, labeled "RDFG". This one is definitely a mechanical relay. You should be able to hear it click when the switch is operated.
The power circuit (through the relay contacts) is fused, in the same fuse block. The fuse is also labeled RDFG.
On the Cobalt and Cavalier, there is one intermediate connector in the circuit between the under-hood fuse block and the window. On the Cav, this is behind the driver's side kick panel.
... Finally getting to the point, on my Cav, the contacts for the defog circuit on this connector were horribly burned, and the connector shell was partly melted. I didn't find an explanation for this. I fixed it by jumpering the circuit around the connector, and had no further problems.
 It's not clear to me if this is an actual mechanical relay, or - more likely - a semiconductor device being represented in that way.