Yeah younger chicks are much more vulnerable to heat and cold issues because they don't have feathers to help them regulate their own body temperature. I hope if you try again you take advantage of all the information on this site so hopefully you can improve your set up.
I'm sorry to hear that. :( It really didn't look good in that photo as chicks don't sleep looking limp that, plus the beak being open isn't normal either.
I don't know if you and your family are planning to get more chicks but please read up on setting up a brooder before you consider getting...
Well considering 3 others already died I am concerned about this one as that doesn't look like a healthy chick sleeping.
If at all possible, get a thermometer tomorrow (or ask your mom to get one, even a cheap one is fine) and get a reading directly under the heat and inside the brooder away...
It's small but the bars look like they should keep the chick contained at least (measure if you can, but ideally they should be around 1/2" or less). Where is the heat, the black dome on the top? Where is the water, the hamster bottle? If that's it, have you seen any chick actually use it to...
A brooder is a box to contain chicks with their heat source so they don't wander off and get lost. In this case you're using a cage, but without measurements or a photo I don't know if there's improvements I can suggest on that front.
Does the UV lamp actually heat up? I have no idea. How...
There's only one chick left? How old and where did you get it? Was it eating and drinking before?
What specifically is the temperature in the warmest area of the brooder? In the coolest area?