Self-Hosted Integration Runtime could not connect to Azure data factory while registering with keys

It seems you hit some network issue. Maybe you can check if you have whitelist azure's IP range.

A connection to the service back end is not possible for the self-hosted IR. Most often, the firewall, DNS, or enterprise network settings are to blame for this problem.

To resolve this

Check to see whether the integration runtime service is running. if it is running and no proxy is configured on the self-hosted IR run the below command in your Windows PowerShell, I will give you glimpse of error.

Code from Microsoft document

(New-Object System.Net.WebClient).DownloadString("https://demofactorypratik.eastus.datafactory.azure.net/")

You can get the above link form Integration runtimes > your self-hosted IR > Nodes > View Service URLs.

Expected result:

If you get a "Remote name could not be resolved" message, there's a DNS issue. if you get an "ssl/tls cert is not trusted" message, then install the public certificate by using Certificate Manager. Go to Event viewer (logs) > Applications and Services Logs > Integration Runtime, here you can find check what's the exact issue.

I can successfully be able to connect Self-hosted IR

Also see, Self-hosted IR connectivity issues