Start with the Dell diagnostics - F12 at powerup. It sounds very likely you've got a dead or dying hard drive. If so, you'll see an error when the diagnostics run - and will need to replace the drive before proceeding with the reinstallation of WIndows.
Windows partitions aren't always assigned drive letter C in Recovery environments. You can use a tool like diskpart to view drive letter assignments, or just try other drive letters and then enter the "dir" command to view the drive's contents to figure out when you've found your Windows partition. However, Recovery doesn't really allow you to recover the registry. It's more intended for restoring a System Restore snapshot, restoring a full system image, or fixing bootloader problems.