HL2 problem

1

I got Half-Life 2 for Christmas, and its being stupid. Now, I know that it needs Steam, and I’ve had it on my PC for a while, but hadn’t updated it for the past few months. When I install HL2, it brings me to steam, and I go to “Games” and it just says “Purchase HL2” or something. So when I click on “REgister a game I already have”, and input the CD key, it says invalid. In my package, the 5 cds were in five different paper holding things. Disc one’s case had the CD key. Th elast part said, and I quote, “…80 HALFLIFE 2” with the 80 being the last set of numbers. How exactly do I input the CD key? Anyone else have trouble, too?