I think I know a fix for this as I've had to do it multiple times.
Go in Steam\SteamApps\common\Team Fortress 2\bin and find "GameConfig". Open the text document and find the lines "Team Fortress 2" and "Half Life 2", and under "GameDir" in both of those sections make sure the address written there is the same as the new location of your game installation. Also change all of the following in both sections:
"BSP"
"Vis"
"Light"
"GameExeDir"
"MapDir"
"BSPDir"
This won't update when you move things to a new drive so you have to change this manually each time. Fortunately its an easy change as all you need to do is change the hard drive letter.