Heya! This problem generally occurs alot (actually, it occurs every time. it's a Spore bug espacially if you got it from not-origin or steam.)
After you have an EA account startup origin and make sure you appear you have bought the game (make sure it appears in 'my games'. if it doesn't, redeem code and enter Spore's code. I'm not sure how to do it from other platforms but if you got it from steam you can access it trough settings option of your game.)
Once the game appears, startup spore.
Make sure you enter your account correctly. (If it says cannot connect to server instead of a fail, try again later.)
Atlesst what I had to do after getting it on Steam but works on other platforms. If you still can't get in, contact EA.