How to remove a broken installation of SQL Server 2008?

After installing the Service Pack 2 of Microsoft SQL Server 2008, the SQL Server failed to start. Trying to repair this, I've done some stupid things, which results now in the situation in which I cannot even install a fresh copy of SQL Server.

Here's actually what happens during setup:

• Setup Support Rules screen (all passed, no warnings),
• Product Key screen (entered a valid product key),
• License Terms screen (accepted),
• Setup Support Files screen (clicked Install).

Than the setup window closes, and nothing happens, no errors, nothing at all. No logs seem to be saved.

What are the steps to clean up the mess and to be able to install the SQL Server without being required to reinstall the whole OS?

I would follow this article, and then once done, I would run CCleaner.
SQL Server 2008 installation fails when you try to install SQL Server a second time

Then try to reinstall (make sure you use the same instance name).

another option - use FIX IT utility of Microsoft:

Fix problems that programs cannot be installed or uninstalled

I've removed all the Microsoft 2008 components via this utility and was able to install it correctly afterwards.

In addition to the answer by KCotreau to this question, for those who are experiencing the same issue, here what I did to be able to make a clean install:

1. Tried to uninstall the old installation with setup.exe,
2. Removed directories related to SQL Server from Program Files (including x86),
3. Removed all references to those directories from the registry. This must be done manually: in some situations, it seems better to remove the whole parent key; in others, only the value must be removed; finally, in some situations you don't have to remove anything, since those keys/values are not intended to be used during setup,
4. Rebooted.
5. Setup started to work, but encountered MsiGetProductInfo failed to retrieve ProductVersion for package during install error, which can be solved either by removing the specified keys (since there are hundreds or thousands of them, be ready to spend hours), or by doing a backup of HKEY_CLASSES_ROOT\Installer\UpgradeCodes, removing the whole key, then restoring it after the clean install is made.

I would still recommend in such situation restoring the last system backup, or reinstalling Windows (both things were impossible in my specific case) if you want to do things correctly.