Games owned by the publisher "Electronic Arts" typically use EA servers. Some games that use EA servers include Sim City, Mass Effect and Battlefield 3. Electronic Arts also has it's own digital distribution service known as Origin. Origin games use EA servers.
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EA games makes the sims games.
Too many...
EA and Microsoft are two entirely different companies. Microsoft does not run EA servers and custom service. To find your origin information, call up a representative from EA (which happen to be extremely nice in the one and only call I've made) and speak with them via phone or email. With all of the necessary information, your Origin may be able to be retrieved.
An EA account is a good idea because it is free and gives you access to other great games. i would recommend making one.
The Serial Numbers for the games in World of EA Games are located on the back of the instruction booklet that it comes with. If you bought it used, or if the instruction booklet is simply missing, you should try to exchange it, return it, or contact EA themselves; they may be willing to give you a refund or allow you to exchange the game directly with them.