Is it possible to transfer Steam games from one PC to another? [duplicate]

Once you have the game in your Steam Library, you own that license and can install it on as many computers as you want*. Simply install the Steam client, log in, and you'll be able to download and install any games you own.

If your program files were recovered, you can save some time and bandwidth after you reinstall Steam by copying what's in your old \steamapps folder to the new one

For example, copy [your backup drive]\Program Files (x86)\Steam\steamapps\ to C:\Program Files (x86)\Steam\steamapps\ (or wherever you installed the client). If you wanted to just copy (all) games between two functional computers you could do the same.

^{*Beware games with additional 3rd party DRM}