Direct sun will cause more evaporation. As stated before, if underwater is the problem, then water should perk them back up within a few hours. If you give them water and they continue drooping... If they've been out of the bins *that* long, I'd say they are probably rotting.
One way to check for rot once the plant has died, pull the cutting and put some firm pressure on the bark, like you intend to rub it off. If the bark slides off anywhere from the soil line or below, your stick rotted from inside out.
Unfortunately, overwatering early can give mold the "in" it needs to sneak up like a ninja and suddenly kill your cutting later on.
Let us know what happens....you should know within 24 hours. Trust me - a little water "should" perk a dry plant right back up. If you add water and it stays droopy a day or two later.... In my opinion, not a good prognosis.