As I'm sure most people would tend to agree: why would you place your system files on C:\? In the event of issues from the OS-level or the drive starts to run out of space, your SQL installation might be in jeopardy if you have the binaries/system databases on the same drive as your OS...

Do you have the option of have your IT department map a new drive (say from an external SAN or other attached storage device)? If you do, then they can copy the drive contents from what's current F:\, rename the new drive, and SQL would never know the difference.