Rather than using the Disk Management you should be able to do the same thing using the Diskpart utility
simply throw the USB stick in
open a command prompt (run as administrator)
type Diskpart (will take a sec to start)
then type "list disk" (gives you a list of all the attached drives, even if they don't have drive letters)
if your 16gb kingston shows in the list
type Select Disk ? (where ? is the disk number)
then type assign (this assigns a drive letter)
If it doesn't show, probably a shortcoming of that model of laptop, perhaps try a BIOS update, and also make sure that you can use other Large USB flash drives of a different manufacturer to test if it's specific to that type of USB stick.
Hope this Helps.