I think you're talking about Warcraft, not WoW. WoW is a MMORPG. Warcraft is a game like Age of Empires, but with peons and heroes and such. It's the one that has the add-on DotA that is HUGELY popular. To my knowledge, you don't download WoW - it's like RuneScape. ie. browser-based. Warcraft is download-able, or it comes on a CD.
WoW comes on a CD, too... You have to download the client and update with patches, etc, etc. Anyway, I don't have a PC and can't really help, but have you tried WoW support? They're pretty thorough.
You'll have to give us far more details if you want us to help, as it stands we can't possibly know what's going wrong for you. Perhaps take screenshots of any errors you get and post them here?