4W seems to be way too insufficient for powering up a 2600 series AP anyway, that should be somewhere around the 12W to 15W range.
Now, I know from the predecessing 1240 series APs that they were quite finicky when it came to PoE. Do you have long cable lenghts in your building? The longer the cable, the more power is lost on the way from switch to AP. Maybe the APs just do not get enough power, and therefore cannot boot.
(I had this problem - too long cabling - with a 1240. It booted, but did not have enough power to start the radio interface...)