UPDATE - The chick has died. My fiancé just came in as I was writing this and told me I don't need to finish my reply. I'm pretty bummed, I was really getting my hopes up that it was just a newborn that needed time to adjust. I don't think taking it away from the hen would have caused it to die, since she was completely ignoring it anyway, and even stepping on it. Anyway - since I've already written it out, here's what I was going to say:
Thanks for all the replies! I will try to address everything. The hen does have a ton of room, and she does move the eggs around from time to time. Lately, she has not been sitting on the eggs during the day as she is so busy with her new chick.. I'm surprised this egg hatched after a week of no hen laying on them - although she may be laying on them at night still.
As for putting the chick back with the hen, I may do that. I'm going to keep the baby under the lamp for tonight just to keep a close eye on it and because it seems like the mother hen is about to give up on her other baby as well. She just seems like she's done and ready to get back in the yard. 7 of my 10 chickens were raised under a lamp so I'm pretty confident I can keep her healthy as long as she starts out that way. I would like the mother hen to raise them.. but I get the feeling she just isn't much of the mothering type. She acts much different than my last broody hen did, and she has seemed to lose interest in the eggs and her new chick.
And yes, the chick was wet when I picked it up. It wasn't drenched or anything, but it was a bit damp and the blood on it's underside was definitely wet, not dried up or old looking. I didn't get enough of a look at it to be sure if there was any sort of cut or opening in the skin, so it's possible it could have just been some fluid from the egg or something. I'm not 100% certain if blood would be common or not. I figured it was common to lose some chicks - I only had 3 eggs hatch out of my first batch which was probably about 10 eggs or so, but I guess I was worried because I've never had any try to hatch but not make it, then all of the sudden I had 5.