@LittleGraveRaven Please try playing in a new admin Windows account. The username should contain only letters and numbers, no special characters, accents, etc. Make it a local account, as in, don't sign into Microsoft, and don't sync with any other services you normally use. You'll be able to sign into Origin and shouldn't need to redownload anything.
If you get another crash, please post another dxdiag and any Reliability Monitor entries from the time of the crash. The errors might be the same as before, but it's better to check. And please let me know if the Reliability Monitor doesn't have any relevant errors: that's useful info as well.