It depends, there are two types of Counter-Strike.
There is a Counter-Strike Source and a normal Counter-Strike 1.6
The Source also have all the files that are necessary from the normal Half-life to play Counter-Strike. However, you can't play the normal Half-Life with the source of Counter-Strike. Let's say if you install Counter-Strike source you only install Counter-Strike.
Counter-Strike 1.6 is a mod of Half-Life. It is basically the same as the source, but you need Half-Life to let it work. So in that case you first install Half-life and patch it to the latest version. After that you install Counter-Strike as a mod of Half-Life(mostly this goes automatically when installing Counter-Strike 1.6, a "cstrike" folder should be created in your half-life folder). Then you can open Counter-Strike by either opening hl.exe and go to the mod section of Half-Life, or by opening the link you have on your desktop(if you checked that in the installation of course).
You say that "hl.exe" is invalid, so it can't be found. So I think you have Counter-Strike 1.6 and not the source. In that case you have to install Counter-Strike as a mod of Half-Life. Then it should work