Search for or run diskmgmt.msc
See if the laptop drive is listed there. Since it *used to be* a C: drive, windows could not use that letter again; the desktop already has a C: drive; so Its my belief that all you need to do is Right Click on the drive in diskmgmt and assign it a new drive letter. Otherwise you may have the option to format the partition if you only wished to do that.
Lastly, you can format the drive during windows installation from the screen that asks you where you wish to install windows to. Simply click the Drive Options link and from the next window you can delete the existing partition. There is no need to make a new one, windows will do that when it sees that the Drive is empty. Simply highlight the...