Need help with Skyrim at Steam

[SuplenC]

Hello. I will start from beginning. So I when I started to play Skyrim along time ago, I downloaded the game from torrent (I know it's illegal but read on) and then after I got all money, about week later, I bought it on steam. I played always on the downloaded version because I have problems with internet and I can't redownload it from steam. I'm using internet key with 20gb/month for 25€ so I can't spend much, no there is no ADSL connection for now in my place. But let's move on to the problem.
Basically I suddenly got corrupted my Skyrim.esm file using TES5Edit and for a strange reason it didn't backed it up. So I thought that moving it into Steam folder, removing the file and scanning it, it will redownload only the file so I won't be forced to download all the game (6.1GB). But moving files into the steam folder doesn't work. It makes me download the whole game once again. Anyone knows how can I repair my game or connect it into my steam account?