When in 2012 did you buy the game and which cover do you have: http://sims3.crinrict.com/en/2014/02/sims-3-base-game-versions.html ?
If you can't play offline, then that's a bug. It always worked fine for me. There's quite a few threads around on this for a while now. Some people just can't seem to offline and I don't know what's up with that.
The Sims was released before Origin so there was no requirement but in Sept 2012 they made a new version, one that is pre-patched to Version 1.42. This version does (as every other EA game) have an Origin requirement. This means that you need to have Origin installed on your computer for the game to run, You need to login into Origin (in on- or offline mode) and you need to start the game through Origin (the shortcuts, ts3w.exe and any programs that require a bypassing of the launcher, don't work with this pre-patched version.
There was a change with one of the patches but all that did was that you now have to start Origin first and start the game from there. The shortcuts don't work anymore (I think that was patch 1.63) but with the new version you always had to start Origin at one point. Before it just worked automatically. Start origin, auto-login and then start the launcher. Now only Origin starts when you click on the shortcuts and you have to manually click play on Origin.
For the old version, it depends if you have the disc or download version but I successfully launcher the game without starting Origin with the download version. Origin is updated but I can't say when it was installed. I'm trying a clean installation tomorrow.
Origin is used to make sure that you buy your game and not pirate them and this is how the future is going to be. Steam does have the same requirements. I was devastated when I found out I have to install Steam on my Computer to play Civ 5.
I don't like this trend either. I do not want Origin on my machine but yet, coming Sims 4 I have two choices: Install Origin or quit the Sims.
I might also completely misunderstanding everything that is said here. English is not my mother tongue but there are just too many issues floating around in several threads and I'm getting lost.