The most likely cause of the administrator's inability to connect to the internet is the incorrect default gateway.
The default gateway is the IP address of the router that connects the local network to the internet. The default gateway should be in the same subnet as the IP address of the device. However, in this case, the IP address of the device is 4.11.17.6 and the subnet mask is 255.255.255.252, which means the subnet has only four addresses: 4.11.17.4, 4.11.17.5, 4.11.17.6, and 4.11.17.7. The first and the last addresses are reserved for the network and the broadcast, respectively, so the only valid addresses for the device and the gateway are
4.11.17.5 and 4.11.17.6. Therefore, the default gateway should be 4.11.17.5, not 4.11.17.1, which is in a different subnet. The routing table, the subnet mask, and the DNS are not the causes of the problem, as they are either correct or irrelevant for the internet connectivity.
References
* 1: CompTIA Network+ N10-008 Certification Study Guide, page 83-84
* 2: CompTIA Network+ N10-008 Exam Subnetting Quiz, question 8
* 3: CompTIA Network+ N10-008 Certification Practice Test, question 3