I sympathize with you. I just started keeping chickens last year and started with 3 hens. I lost 2 last year to predators, and had to wait many months before I could find chicks again. The hen I had left, Ethel, was kinda depressed a lot and hung out by my sliding glass back door when I was home. She would even knock (peck) on the door to get my attention. I spent as much time with her as I could, but she still seemed really lonely. I ended up having to quit my job due to medical issues, and started my own business and now work from home. I spend plenty of time with her now, and she perked up and got back to her usual self. Even if I can't go outside, I will leave the back door open and she will let herself in. lol About 3 days ago, I got 10 chicks and she doesn't seem to like them at all. I think the problem is, she's gotten used to being a loner. I hope she eventually gets over it and soon. Your chick might do ok even for a long while if you can spend a lot of time with her, but I wouldn't suggest making a chicken go the rest of its life alone from other chickens. If you can get all your materials for free, it wouldn't hurt to make your coop a little bigger in case you want to get your chicken some more friends one day.
I agree about craigslist's free section, but be careful. I've gone to pick up "free" items to get there and find the person decided they wanted to get paid for the item(s), or you get to where you are going to find that they didn't tell you they had the items in bulk and suddenly you can't just have what you need for free, but you can have 5x what you need for a "steal".
Another website you might want to try is freecycle.org. You can search in your area for things people are truly giving away for free, or you can post a wanted ad for what you're specifically looking for. Personally, I've had a lot better experience with this site. Overall, I've had a lot less trouble with shady or downright dishonest people, and people have gone out of their way to help me. I posted a wanted ad once, and the person who responded didn't have what I needed, but a friend of theirs did. They got me in touch with their friend and I got what I needed for free.
One more suggestion... If you want to go the wood pallet route, try checking out mom and pop hardware stores, feed and grain stores, and plant nurseries. Especially plant nurseries. Just whatever avenue you take, make sure it's mom and pop. Bigger chains like Lowes, for example, usually have to return the pallets where they come from so they can be reused. The reason I especially suggest plant nurseries is because just about everything they get comes on a pallet and its usually a hard wood, like oak. There's a mom and pop plant nursery around the corner from my parents who give almost all of their pallets away. They keep just a few here and there for store use. The owner says he has to give almost all of them away or they would be covered over in pallets. They are oak, for holding heavier materials and have been heat treated, meaning no nasty chemicals. Heck, I've even stopped by places that had pallets laying around like they were going to be thrown away. I stopped, looked them over, and if they were to my liking, asked if I what they were going to do with them. If they said throw them away, I asked if I could have them, and they said yes. Just keep your eyes peeled. Hope this helps.