@GamerGirl101z I'm sorry that you're having such trouble with your codes. For what it's worth, you absolutely have the right to replacement codes, either from EA or Target. Since Target is an authorized retailer, someone has to honor your purchase. You might try sending the transcript of your chat with EA support to Target and requesting new codes. Or you could ask for your money back, since you didn't receive a working product.
Sometimes it's easier to register codes on the Sims 3 store site, rather than within Origin. Codes for expansion and stuff packs are 20 characters long, and you'd need to use the link to "Register a Game," rather than "Redeem a Code," which only asks for 16 characters and is for worlds and other bonus content. Both links are at the bottom of the store site page.
But I can understand why you'd want to give up dealing with Origin entirely; it can be a massive headache for many players. Discs are great, as long as your computer can read and authenticate them, but that's not always the case. You'd also need a base game disc manufactured before September 2012; the ones made later require that Origin be installed to "manage" the game install. So you'd wind up right back where you started, on patch 1.69 and needing Origin to be running to launch your game.
If you're serious about repurchasing TS3, Steam would be significantly cheaper right now. The base game and packs are $5 each right now; the sale ends January 3 at 10 am PST. There are a couple of even better discounts available too:
https://store.steampowered.com/bundle/1247/The_Sims_3_Bundle/
https://store.steampowered.com/sub/19071/
You could also just buy the packs you're missing—you'd receive CD keys from Steam, which you could register in Origin just as you wanted to use your Target code. You'd need to buy a copy of the base game as well, but if you registered it, you'd receive 1,000 free SimPoints. I know this works because I'm one of the many that has done this, although I added my codes through the store, rather than Origin. (I don't trust the app either.)
Anyway, if there's anything else I can do to help you with this mess, please let me know. If you would in fact like to try to recover the content you bought from Target, I can ask someone from EA what else you should do. Like I said, you have every right to the content you bought from an authorized retailer.