Any ideas for an unresponsive iDRAC on a PowerEdge R640?

First, confirm whether iDRAC is set to use the dedicated management port or a shared host port, and make sure the cable is in the port that matches. Check the switch port's VLAN and other settings too. Other hosts working on the same switch doesn't rule out a problem specific to this port.

The link and activity lights are useful, but they don't prove iDRAC is responding at its configured address.

Try isolating the network path. Connect a laptop and the iDRAC port through a small switch, give the laptop a static address in the same subnet, and try the configured iDRAC IP directly. That takes the usual management VLAN and routing out of the test.

A packet capture on the laptop can help show whether the iDRAC sends or responds to anything. If it works on the isolated setup, move back toward the normal switch path and check the cable, port and VLAN configuration.

Before wiping everything, try changing the network settings and then changing them back. That may force the values to be written again even if the settings screen already shows what you expect. You could also try DHCP on a suitable network and see whether it obtains an address.

For a software-side check, try RACADM locally from the host OS, or from a suitable boot environment if that's available and permitted. That can help distinguish an iDRAC communication problem from a network-only problem and let you inspect its configuration.

If you don't have host credentials or permission to boot another environment, pass that part to someone who does. An IPMI tool may also be worth trying where local access is available.

A factory reset is a reasonable next test if the network checks don't turn anything up. Record the current settings first and plan for restoring them afterward, since you'll need to configure access again.