I bought Diablo 3 in the CD version and now, even after installing it, I can’t get past level 13.
Hello:
You’re playing in Starter mode… a free mode restricted to the very beginning of Act 1.
To play the version you purchased, you need to redeem the authentication code(s) for D3… see https://eu.support.blizzard.com/en/article/11263 for details.
If you’ve done that already… then you need to log in with the e-mail that was used when you first redeemed the code(s).