Everything can die if they don't eat. lol Snakes can go months wiout eating, so don't stress too much about it.
BPs don't need UV lights. I would take it back to the pet store and then get a basking lamp (if you don't have one already). Go with a 50 watt or something that can make the hot end of the tank around 33-34C. The rest of the tank should be around 27C, but never under 24C.