GTA IV will not start

Solution 1:

Run as Administrator

First, completely exit Steam, and right-click on the shortcut which you use to launch Steam and select "Run as Administrator." This step may be enough to fix the problem. If not, continue below:

Additional Installers

You may need to manually run secondary installers required by this game. Exit Steam entirely. Browse to your Grand Theft Auto 4 installation folder (Usually C:\Program Files\Steam\steamapps\common\grand theft auto iv\)

You will need to run each of the following installers:

...\steamapps\common\grand theft auto iv\Installers\DirectX_jun2008\DXSETUP
...\steamapps\common\grand theft auto iv\Installers\DirectX_Mar2009\DXSETUP
...\steamapps\common\grand theft auto iv\Installers\vcredist_x86

Games for Windows Live

Also, install the latest version of the Games For Windows Live software, which can be found here: http://www.microsoft.com/games/en-US/Live/Pages/livemarketplace.aspx

Restart your computer and test the issue again. If you continue to have difficulty, run this installer:

...\steamapps\common\grand theft auto iv\GTAIV\Activation\SteamActivation 

References

Taken from this steam forum post. In addition, there is another thread of a huge list of GTA IV steam issues which you can find here.

Solution 2:

If your GTA 4 is not running anymore, download and install the Windows Live Client.

This solved it for me.