if you still have the old comp, there are a few options for you:
1. network them together and just copy/paste the wow director to your new computer.
2. make a DVD or set of DVDs or CDs and copy the wow directory from old to new.
3. copy just the Interface, WTF, Data directories and the latest patch.exe, not the downloader for that patch. might not be a bad idea to grab all of the patches, but you could just grab the one massive patch off of 3dgamers.com
4. take the old hard drive out of the old computer, put it in the new computer, making sure it is not set to master and put it on a separate channel (if IDE this is easy, if sATA not as easy, but still simple enough) and copy the data from the old drive to the new drive inside your new computer.
#4 will be the fastest way, with #1 being the second fastest followed by 2 and 3 respectively.
to many options to make it easy for you. the nice thing about WoW is that it does not touch the registry so as long as you have all of the files in the wow directory, you are golden.