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When troubleshooting a Telnet login failure, the first operation that should be prioritized is to check whether the client can ping the server. This step is crucial because it verifies basic network connectivity between the client and the server. If the client is unable to ping the server, it indicates that there is likely a deeper network issue at play, such as a network outage, incorrect routing, or firewall issues that may be blocking traffic between the two devices.

Establishing basic connectivity is a vital first step in any troubleshooting process. If the ping test fails, there is little point in checking for login limits, ACLs, or access protocol configurations, as these checks pertain to the application layer rather than the fundamental network layer connectivity.

Once connectivity is confirmed by a successful ping, further troubleshooting can then focus on the other potential causes of the login failure like checking the maximum number of users, examining the access control lists (ACLs), and ensuring that the VTY settings are correctly configured for Telnet connections.