The default for any install of XP on a clean hard drive is C:, so I have no idea hiow you have a C: partition (which you say doesn't exist) and an H: partition (which you say is the actual hard drive.
In any case, either one of two things can solve the drive letter for partition thing...
a. Do a repair install of XP.
b. Do a clean install of XP.
The fact that something went wrong on what should have been a simple process...would trouble me.
I suppose that the important thing is to ensure that no other drives are attached when doing either the repair or the clean install.
How to perform a repair installation of Windows XP if Internet Explorer 7 is installed - http://support.microsoft.com/?kbid=917964
How to Perform a Windows XP Repair Install (Stevens) - http://www.michaelstevenstech.com/XPrepairinstall.htm
XP Clean Install, Stevens - http://www.michaelstevenstech.com/cleanxpinstall.html
Clean Install Procedure with Illustrative Screen Captures - http://www.theeldergeek.com/xp_home_install_-_graphic.htm
Clean Install Windows XP - http://www.theeldergeek.com/clean_installa..._windows_xp.htm
Paul Thurrott's SuperSite for Windows Windows XP Clean Install (Interactive Setup) - http://www.winsupersite.com/showcase/windowsxp_sg_clean.asp