I purchased the S3 license, and after a day my account went back to the demo version, even though I also had proof of purchase.

Contact developers here: https://www.lfs.net/mailus
Make sure to include all relevant information (proof of purchase mainly, date and method of purchase etc.) so they can check what happened.

I sent all my purchase information to https://www.lfs.net/mailus, why am I not getting a reply?

Hello Mahmut005,

Live for Speed sends you this email as a confirmation that you have unlocked Live for Speed in S3 mode.
The following IP address was used during the unlock :

You currently have 2 unlocks left.

FYI : Every friday morning you will receive an additional unlock to your LFS account, unless you already have two unlocks available at the time.

Have fun!

The LFS Team

Security note : If you, the account owner, did not just unlock LFS, you are strongly advised to change both the WEBpassword and GAMEpassword of your LFS account. You can do that at any time by logging in on our website and going to your account details page.
...