From this list, look under "Other Games" and see if "Earth's Special Forces" is there. If it is, just double-click it. Using Counter-Strike doesn't have side-effects, no need to go buy a copy of Half-Life or anything.
I generally don't have that happen to me...
Here's an idea:
Place an icon on desktop, have the target be:
"C:\Program Files\Valve\Steam\Steam.exe" -applaunch 70 -game esf
Are you sure your cd key is valid? Sometimes people can open boxes and steal cd keys and use them. I had this problem when my cd key was invalid, Try entering your cd key in the "Register a product I already own" window that pops up when u click it on the Browse games thing (If that makes sense.) Enter your cd key there. If you've already entered your cd key then it'll tell you that you've registered your product and then I don't know what your problem is. If it tells you that your key is a duplicate then someone has nicked your key and you need another one. If it registers your product then all you need to do is reinstall ESF (and if you want other Valve games just install them too) and you should be good to go.