It looks like this problem has occurred a lot over the last few days, from the number of posts on some variation of this. It would be nice if an EA representitive would get online and help.
On my particulart version of this problem, I bought the game for my daughter,( runs fine on her computer (XP)). I downloaded to mine also and logged in under her name to double check the content before she played it. After seeing how fun it was I created my own account and bought a second copy for myself. Logging into my account the game would start,(Win 7 ulimate 64bit), but immediatly crash before the first splash screen came up. I uninstalled everything and reinstalled not once but twice. Same thing. What gets me it was fine running under her account.
I'm going to try your method after it finished downloading for the third time.