GS724TV6 - Refuses to get DHCP address non 192.168.0.x address

In the subject, you say "Refuse" - are the DHCP requests ever reach your LAN, and the Verizon FIOS router LAN and it's DHCP server, and you have some indications from that DHCP server that is has assigned the intended IP address?

JonJonJonJon wrote:

They take the default address of 192.168.0.239

This is the Netgear default IP address config if the DHCP client does not recieve an anser on the LAN.

JonJonJonJon wrote:

When I configured one to 192.168.1.30 with a gateway of 192.168.1.1 (the Verizon Router) it would be seen when I plugged it into the network.

Permitting the GS724Tv6 management VLAN (default VLAN 1, ...) is really connected to your LAN - yes, of course.

JonJonJonJon wrote:

- I was able to configure a PC as 192.168.0.1 and connect to them

When doing so, this PC was connected to the LAN, or had used a temporary direct link to the GS724Tv6?   

Based on your problem description, I guess that was a direct connection...

How and where are your two new GS724Tv6 connected to? Thats the point you should start investigating...

JonJonJonJon wrote:

The Network Discovery Tool doesn't see the device on either the 192.168.0.x or 192.168.1.x configurations

The NETGEAR Discovery Tool can make use of NSDP (NETGEAR Switch Discovery Protocol) and UPnP (Universal Plug and Play SSDP protocol) to discover NETGEAR devices.

In combination with these recent switches - NDT depends on a working network connection, the switch and the PC need IP configuration in the same subnet - its pure SSDP.

The legacy NSDP - able to discover any device on a transparent layer 2 network - is unlikely implemented 

Your other GS108Ev4, and GS316EPP switches are supporting also NSDP, unless the admin has explicitly disabled the NSDP discovery function.