Help! Sims 3 won't start

This is my first time posting, I'm desperate and hoping someone here has faced this before or knows a workaround. I've been locked out of my Sims 3 base game and expansions (which I've owned for 9 years)

The Situation:

The Tech Glitch: My game used to work fine on my old laptop and worked around 4 times on my new laptop. Now, when I click "Play" in the EA App, a sign-in pop-up appears, but there is NO place to type my password. Just a grey screen asking me to sign into an EA account even though I'm signed in at the start of the game, in the EA app, online into EA.

Missing Expansions: Before it froze, only 3/5 of my packs showed up in "Expansions and Stuff," even though the EA App said they were downloaded in Add ons.

Origin instruction: When I uninstalled the EA App to try running it directly, the launcher asked me to open via Origin, not EA. This feels like a migration error.

The Support Nightmare: After spending 8 hours with 9 different agents, they finally told me a payment from May 25, 2017 is "not validated," so my whole game is locked.

They wouldn't tell me WHAT item the payment was for.

They refused to let me play just the base game even after I said I didn't care about the missing packs.

Confusing Advice: One agent kicked me out of the chat and said "Go ask Steam support." BUT I don't own the game on Steam! I never linked my accounts. The game is clearly on the EA App/Origin.

Impossible Demand: They told me to go find a bank statement/receipt from 10 years ago to prove I paid. (PayPal and banks don't keep those easily accessible!). 

Why I think this is a BUG, not fraud: I found a receipt from June 2017 for the University Life Pack, but the packs failing are Pets and Seasons. Blocking the base game over a dispute for a different DLC seems wrong. Plus, the "Login window with no text box" looks like a known software glitch.

If anyone can help it be greatly appreciated, thank you. I've attached the sign in page that opens.