I installed TS3 in 2011 and at first it was fine. But it was some time after that (maybe summer 2012?) that some patch came (the one that introduced this, see below) and it slowed down the game to a ridiculous level, and it hasn't recovered since.
It's so bad that it generally takes 30 minutes to start the game (from clicking it until I enter a neighborhood), with switching neighborhood easily taking 15 minutes, saving takes 10 minutes, and going anywhere on the map is a pain. Forget about large houses. Every location takes a lesser eternity to load.
I read that the only way to get rid of a patch is to uninstall the game and reinstall from scratch. So I did that. But I have four expansion packs, two new ones bought and installed a long time after that patch. So when I reinstalled the last two expansions, the game forced me to also reinstall all those patches... and I'm back exactly where I started.
I take it you want to know specifics about my computer, but you'll have to tell me how to check it. I just know it's Windows 7, from 2009, is not very powerful and hasn't gone through any "upgrades" in hardware since acquired. (Except yes - a new graphics card.)
There has to be some way to fix it, even if it's to get new hardware.