Avoiding drive letter problems is one of the main things we have to consider when cloning and moving Windows and there are a few measures we can take before hand to prevent such issues from arising. For example we can hide partitions from Windows so that letter allocation won't take place, or we can delete Window's memory of previously allocated drive letters so the old associations don't come into play. This is partly covered below, but is more fully explained in this article and so if the recovery procedures detailed on this page fail for you then perhaps a bit of prevention may help in any following attempts you have at moving Windows. There are of course other boot issues to be overcome when moving a new-generation Windows operating system and knowing a bit about the new boot files is key to an understanding of those.
Once you have your wrong drive letter then New task ... again and this time type in and run regedit and navigate to the key described in the screenshot below. Right click on the \DosDevices\ entry that has your letter and choose rename and change the letter to the one you think it should be (usually C:). If the registry already has that letter assigned to another DosDevices entry you will need to change that one first to free up the required letter. You can make it anything for now that is not currently in use as you can change or remove it later from Disk Management once you are fully into Windows.
If you just can't get Disk Management or Regedit to open for you in the steps detailed above, even in safemode, then try 'Safemode with Command Prompt'. Note that from Win7 in safemode you have to tick the option 'Create this task with administrative privileges'. If you still can't get Disk Management to open but regedit works then you can make an educated guess as to which DosDevice entry is your desired target and change its letter and try rebooting. If you don't have success first time then repeat the process with each DosDevice entry until you get the right one.
Another option you can try is to just delete entire lines in the MountedDevices key, which will force Windows to completely rebuild them on reboot. You can in fact delete the entire contents of MountedDevices (except the first line) and this may well do the trick, as in the absence of any previous letter allocations it is normal procedure for Windows to make its own partition the C: drive. Clearing out the MountedDevices key is something that can be done in a fully functioning Windows install in order to try and cure certain letter allocation problems, or as a preemptive step before moving Windows so that letter allocation problems are avoided. Please be acutely aware however that in normal circumstances changing or deleting items in the MountedDevices key should not be tackled lightly and it is only safe under certain conditions. In our case here with an already non-booting operating system we have little to lose and we should still be able to recover things manually by changing each line individually till we get it right and give our partition the correct letter.