If I were you I would find some way to measure the temperature down at the chick level, at several different spots in the brooder. I know too well how easy it is to assume the temp is steady everywhere. I had several problems with that myself. To keep myself from making the same mistake again, I had a thermometer in each section of the brooder. I checked each one at least once a day, usually several times. I still nearly chilled my birds once, and nearly set their bedding on fire another time. If your chick is lethargic and chirpy, I would really question the temperature; just from my experience.
Also, the crate they are in, is it an open cage like one, or is it one with plastic bottom and top with holes in the side?
If it is an open cage, you might want to put up a windbreak(cardboard or paper, or something to prevent drafts into the brooder.
Is there protection from the cold of the basement floor? I mean a layer of insulation between the floor of the brooder and the basement floor.
If it is the plastic kind of crate, is there enough air circulation? Does it smell? If it does, there might be fumes building up inside that are irritating to their lungs. Not sure what you would do about that, though, other than making another brooder. My setup was pretty easy, very rough, I kept them in my garage, and I had a play yard(for kids) that I used as the support for one; but they were basically cardboard taped together and made into circles, ovals, whatever, and duct taped to the floor. They had about 3 inches of bedding between them and the concrete floor, mainly to hold in the heat. I think I uploaded some pics here, if you were interested.
Is there a chance your chick is eating some while you are not watching? It does have access to a food dish all the time, right? Can it find the food easily? Maybe try sprinkling some chickstarter on a white napkin in front of the chick, maybe that can trigger it to want to peck.
I hope this is somewhat helpful to you, I am really tired right now and can't seem to get the words out the way I would like.
The cage is sitting ontop of a table. It is a wire kind, not plastic. It does not smell and has good air circulation. I put tinfoil about 6 inches up the side of my cage to mainly keep the chicks from getting out. We have a woodstove in the basement too so she is not cold. I will take the thermometer and move it around the brooder, but I am pretty sure the temperature is fine. But it won't hurt to check I suppose. I am pretty sure she is not eating when I am not looking because she doesn't poop. I was holding her for a couple hours last night and she didn't poop at all. Which told me she wasn't eating even when I offered her cooked egg yolk or chick crumbles.