Howdy!
In most cases we have found this issue to be related to the order not being completed yet, for example if you just purchased the game. Double check the order status is completed under your Transaction History.
After that this can be multiple issues either the Battle.net Desktop app cache is corrupted not seeing you have access to the game or can’t be updated properly due to a unstable connection issue. I would recommend to ensure the following steps have been completed. Given SamHa11 you couldn’t connect to our site which is currently up and running with out issues this is for sure likely a connection issue:
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Shut down the PC. Power Cycle the home network’s modem and router to refresh the connection to all devices on the network and to the Internet Service Provider. Steps on how to do this can be found here: Power Cycling Your Network Devices - Blizzard Support
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Once the network is back online, turn back on the PC. Flush the DNS cache using the commands here: IP Release, Renew, and Flush DNS - Blizzard Support
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Close the Battle.net Desktop app. Press (Windows key + R) type in: %ProgramData%
Press the Enter key. Within the folder that appears delete both the Battle.net and Blizzard Entertainment folders.
Now run the Battle.net Desktop app and login. Your Battle.net Desktop app under the Diablo II: Resurrected section may say “Install” instead of play after doing these steps, select: Locate this Game and select the Diablo II: Resurrected folder, the client should update to play then retest.
If the issue continues from here you may wish to go deeper into connection troubleshooting following the steps listed Here. Then run a 10-minute WinMTR to host IP: us.patch.battle.net Copy the text to clipboard after 10 minutes and post the data back here for review.
Thank you.