A computer that displays an IP address starting with 169.254.x.x has failed to obtain a valid IP address from the DHCP server and has assigned itself an automatic address (APIPA). This can be caused by a DHCP server failure, network connectivity problems, faulty network hardware, incorrect configuration, or an exhausted DHCP address pool. To diagnose the issue, check the IP configuration, verify network connections, test DHCP renewal, and ensure the DHCP server is operational.