@Cuhhhree I see a Browse button below the text field when I'm typing a reply; it's next to a paper clip icon. But it doesn't matter—you clearly had no trouble attaching the dxdiag.
I can see why you'd have so much trouble running TS3. Your computer's specs are pretty underpowered—you have only 4 GB RAM and a weak integrated graphics card. Still, you may be able to run the base game and the two packs you've installed. (Late Night is relatively mild, and none of the stuff packs add much to overhead.) TS3's requirements aren't all that high by current gaming standards, but it doesn't adjust well to lower specs.
Your best bet here is if you make sure your computer is only running the game, and nothing else. It's also a good idea to trash the TS4 game folder in Documents\Electronic Arts, since it's always possible that you have a corrupt file in there somewhere. Then, right before you want to play, restart your computer; this will free up as much RAM as possible. Don't open any other apps, not even a browser window. Sign into Origin and then put it in offline mode, and disconnect your computer from the internet. Then launch TS3.
When you get to the Main Menu, before pressing play, go into game options and turn off memories, the in-game shopping experience, and the hidden object interactive loading screens. All of these increase the RAM load on the game. Then press play. If it doesn't work, repeat the same process (starting with rebooting your computer), but when you get to the Main Menu, turn all your graphics settings to low and quit, reboot, and launch the game again.
If you can play, you can probably turn some graphics options back up, although leave water and high detail lots at the minimum settings. (These take more resources than the other settings.) And make sure to only change graphics settings at the Main Menu, then quit and relaunch the game, or else you'll see some very strange graphics glitches.
Again, I'm not sure that your computer can run TS3 at all, unfortunately, but this is your best shot. It's really too bad that the game handles weaker systems so poorly, but there's not a lot that can be done about it.