M4250 configuration needed to allow DHCP passthrough

Hard to imagine an out of the box or factory defaulted  M4250-26G4F won't pass traffic, e.g. no DHCP from the primary switch - there is no special configuration required. Especially as its connected at the same location like the previous unmanaged switch.

Start with a basic check if the uplink port (connecting to the main Cisco) has link LED indication at least - regardless if it's a managed or an unmanaged switch. 

The minimum I would suggest is to define the M4250-26G4F MAC on the DHCP server, so it will receive an IP address. It's not an inexpensive unmanaged switch, worth taking control, learning -and- properly managing your network. This includes regular firmware updates at least, and ensure it remains reachable from your network admin workstation. 

One might guess, also the main Cisco switch acting as a DHCP server, and connecting at least the new Netgear AV switch, should be properly managed, too. Just like all other AV devices.