Lucibel: As I discovered with LucasArts, these companies outsource their support to 3rd party organisations. The support at LucasArts didn't know The Secret of Monkey Island was being sold at Direct2Drive, and kept saying it was only available on Steam.
Anyway, if you check back a few pages you'll see my experience of the EA store. Thumbs up.
Navagon: Did you get immediate access to your games from payment? Only I completed the checkout, but no confirmation emails or anything. They mentioned it could take 24hrs. But they say that about a lot of things (and it clearly isn't true).
I guess I'll have to email them for clarification. I just hope I get a more timely response.
Oh and Lucasarts are completely hopeless when it comes to customer support.
I received email receipts and was downloading straight away. You could login into the EA downloader with your email and password and see if it's showing up to download yet. If so, you can at least start downloading, though for Mass Effect you will need the serial they email you. For Dead Space, you won't need a serial.
Once it's all downloaded though, it should be a happy experience. Be sure to backup the game files; if you're using Vista you'll have to show hidden files, then go to Program Data\Electronic Arts\EADM\Cache folder.