If the d3dx9_31.dll is in the C:/Program Files/Electronic Arts/The Sims 3/Game/Bin folder then I would suggest maybe trying a .dll file from a different location as the one you are using might be corrupted, which has been known to happen and cause problems. If the .dll is in the right spot, then it is going to hard to diagnose without seeing your computer, and I would suggest if you know someone with experience with TS3 and/or computers, you might try asking them to diagnose in person for you.
It is in the /Game/Bin folder, but what other location should I try it from? I downloaded it from here...
Windows Update downloaded an update that crashed my whole system. I lost everything and had to reinstall the operating system. So I've played the game with AweomeMod before the crash and I will tell you, without the mod this game is pretty much a waste of money. I'm really disappointed, but thanks for trying to help me.