To wipe TDU completely you must:
Uninstall the game via Control Panel > Add/Remove Programs (XP), Control Panel > Programs and Features (Vista) or Control Panel > Uninstall a program (7) or Settings > Apps > Installed apps (11)
[Note: Test Drive Unlimited may not appear in the Control Panel if you are trying to remove an illegal version of the game, which you shouldn't have in the first place]
Clear the folder you have the main TDU files in (default is C:\Program Files (x86)\Atari\Test Drive Unlimited (The '(x86)' part is only applicable if you are running 64-bit Windows)
Delete (or rename/backup) your C:\Users\YOU\Documents\Test Drive Unlimited\ folder
Delete (or rename/backup) C:\ProgramData\Test Drive Unlimited\ (This folder contains your serial keys for the game and car-pack)
Delete any remaining registry keys for TDU located at HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Atari\TDU (The 'Wow6432Node' part is only applicable if you are running 64-bit Windows)
ProgramData - This folder is hidden. (Instructions for showing hidden files/folders on Windows: XP, Vista, 7)
HKEY_LOCAL_MACHINE - This refers to editing registers on your machine. Be careful, editing registers is very dangerous especially if you don't know what you're doing.
To edit registers on Windows:
(XP) Go to Start > Run, enter "regedit.exe"
(Vista) Go to Start > All Programs > Accessories > Run, enter "regedit.exe"
(7) Press Windows key and R, enter "regedit.exe"