I have seen Windows setups where the boot drive was something other than C, but that is usually caused by either changing motherboards or transferring a hard drive to a system other than the one it was installed on initially. My guess is that this is what happened. You are now finding out why this situation justifies reinstalling Windows. It's never a good idea to have the C drive unassigned. You get serious drive conflicts that way.
That said, you haven't shown me the capture of Disk Management. I wouldn't ask for it if it wasn't important. Please post it. We need to know what type of drive the C is. My guess is that it's the virtual CD drive that U3 installs. On that subject, I would disable U3 on the drive. Most people don't like it anyway. You can find out how by checking the flash drive maker's support site.
Honestly, I would disconnect all removable drives from the system and reinstall Windows properly. Before you do, be sure that BIOS setup boot sequence is set properly so that the hard disks are first. If you set "Removable drives" as the first boot device, you'll end up right back where you started.