mholmes3038 EA has never supported Sims 3 (or any game really) in Linux. The fact that games work at all is due to the efforts of the Linux community and sometimes companies like Steam.
Having said that, it sounds like your new computer might be missing a resource that Sims 3 needs. The main ones are DirectX 9, VC++ 2005 x86, and .NET Framework 3.5. So see whether you have those, or the Linux equivalents, already installed, and if not, get them.
Beyond that, I can't help with Linux issues because I have no experience with any flavor of Linux at all, let alone knowledge of how to run games there. I've seen a few comments about using it on the NRaas site and heard rumors of Linux users on MTS. So those might be better places to ask.