If the fans don't work even when connected to the always-on fan connectors, then the fan voltage supply has fused. This happens if you short the two pins of one of the fan outputs together.
To fix it:
First check that you have the jumper in the correct position in the 3-pin fan voltage selector jumper block.
If you have a version 1.03 or later Duet, check the 1A blade fuse visually or with a multimeter, and replace it if it has blown.
If you have an older Duet, use a multimeter to check that there is continuity between the pin at the VIN end of the fan voltage selector jumper block, and the VIN+ terminal. if there is no continuity, then a via in the PCB trace between those pins has fused. You can bypass it using a piece of wire on the back of the PCB. There is another thread about this issue that includes a diagram.
Before applying power again, check that you have resolved the short that caused the problem.