One of the below three situations describes your problem:
#1 You insert a USB stick and nothing happens. You know the USB sticks work with other computers.
#2 You insert a USB stick and nothing happens for a while. There is a long delay. You know the USB sticks work fine with other computers.
#3 You plug in a USB stick but you hear a different sound from what you are used to. You hear a sound with three notes with the third note that is quieter than the first two. You can hear it at 13-second mark of this 14-second clip.
The YouTube video above shows "USB Device Fail" when it plays the sound you are experiencing (and descibed above at the 13-second mark). It is supposed to signify the USB drive insertion failed; this sound can be a "false negative" or benign. In your case, there is indeed no drive letter appearing in Windows corresponding with your physical insertion of the stick. What should you do?
If the problem is intermittent and happens infrequently, the solution may be to just live with it. Otherwise you may need to reinstall the Windows OS. If reinstalling the OS does not work, you may need to purchase a new computer or replace the USB ports inside the computer. If the problem is intermittent, the problem would likely be solved by reinstalling the Windows OS. If none of the above are acceptable, you can read this external posting.