I was at my church today and was called into the office and asked to fix the computers because they all just went down. It took about 2 hours of diagnosing but I got lucky and fixed it with the network switch.

Am I correct and say if the computers power up and people can do things locally, but can't access printers, other computers, and the internet, it's not a computer problem but rather a Network problem?

the computers make up the network so theres a chance the network is down because of them, but if they all fail its more likely to be hardware connecting them together