Are they dry now? If they are, you should be able to tell if they are wet or losing down. If they are dry but still look wet, you might try fluffing their down. If there's something on them, you can try getting a rag damp with warm water and cleaning them off a bit, making sure to dry them thoroughly.
Sounds like your set up is fine as long as it's warm enough. The only thing I could think of that might cause this is if the bedding is too wet or filthy, but I really doubt that because it sounds like you are doing everything you're supposed to.
Oh - and make sure your waterer is secure so it won't tip over and make everything wet. Chilled chicks = death and all kinds of problems. And make sure it's shallow so that chicks can't soak themselves. Folks sometimes put marbles at clean rocks in the bottom for a few days until the chicks are bigger.
