How it looks:

At the game start, when you enter search for any of the game modes, you get screen that it started, but ping for the search shows <350ms.
Cause:

Activision system, for some reason, gave your account a so called "shadow ban".
There is no known and confirmed reasons for this issue, and many players claimed to have recieved it without any reasons whatsoever, no cheating, no misbehaviour, no rule breaking, no cloud services.
You can see discussions regarding this topic on Reddit and Blizzard forums.
Officially, Blizzard doesn't recognize this problem.


Solutions:

There is several ways to resolve this issue:
1 - Wait for 1 to 7 days, this value can vary from account to account, and is not confirmed.
2 - Register a new account, in case of Warzone, game is free, but it comes with stat reset.
3 - Contact Activision support, they seem to be able to lift this ban.

Need more help from the support team?