Open the start menu.
Type "dxdiag", and hit enter.
Click the "Display" tab.
Take Screenshot.
Post.
Your chipset should be ATi Radeon HD 4200. It should be able to run L4D2.
Your computer seems qualified enough to run it, but here should be a solution.
Close Steam, then try opening "C:\Program Files (x86)\Steam\steamapps", and deleting "left 4 dead 2 client.ncf", "left 4 dead 2 common.ncf", and "left 4 dead 2.ncf".
Re-open Steam.
Click Left 4 Dead 2, then click the install button. (do not worry about the 13GB download, it only redownloads the above files, then reads the rest of the files to verify)