Finding DHCP server address

Are you sure en0 is an active interface? Try just;

ifconfig

This will list all interfaces on your Mac. Find the one that has the IP address and use that interface index. Depending on your Mac model, Ethernet may not be en0. Once you find the interface index then try ipconfig getpacket again.

Well, if it is just your system connected to the switch and the switch is providing a valid lease, you could try pinging the broadcast address. Ping the last address in your range. Example: ping 192.168.0.255. Check Network Preferences to get your specific subnet address. This should, in theory, reveal any device on that subnet.

Then you can try running an arp -a and compare MAC addresses if needed.

What switch brand? Is there a hard reset switch on the unit?

This is fundamentally a Netgear-specific question, and not something that particularly involves OS X.

169.254.0.0/16 is in the self-assigned IP address range. You're not getting an address from the switch, which implies that the DHCP server isn't working right, that you're not on a vLAN where the DHCP server is working, or the DHCP server is disabled. Given that device is a managed switch, it's anybody's guess how the ports and vLANs and the DHCP server are configured.

If you've not already done so, get the manual for the switch and read through that; that'll give you some idea of the interface and capabilities and norms for the device.

Some of the few discussions on the hardware reset process are here, here and here in the Netgear forums, and particularly a blog post here, and it looks like there are registration-required Netgear forums for this series switch that might have additional discussions.

Based on those Netgear forum discussions, there are some bricked switches around, too.

As MrHoffman says, the fact you are 'getting' a 169.254.x.x. address means your Mac is not actually getting an IP address from a DHCP server but is generating its own self-assigned IP address.

The default configuration of a managed switch would be to not act as a DHCP server so the fact it is not doing so is perfectly normal.

You could try setting up a proper DHCP server on your network either on a computer or using a router or firewall. It maybe that the switch would then itself get an IP address from that DHCP server.

It is also common for switches to first have to be configured via a serial port connection to give it its initial network settings. This is possible on a Mac if you have a USB to serial adaptor and suitable terminal program. (I have used a Keyspan USB adaptor and ZTerm.)