The DnsIP would normally be your router IP, The device IP you should be able to choose, I would do the following:
Check the IP address on your PC, and that of your router (gateway on the PC)
If the router address ends in 254 and the PC address id low (say between 1 & 20) then I would opt for somewhere in the middle, say 130. If the router address is low and teh PC address is high I would still opt for somewhere in the middle. Before setting that address on the Arduino try and ping it from the PC if it constansly times out you should be OK, if it returns successfully then there is something on that IP and you need to choose again.
Do you have many things on your own network? One other clash that can cause problem is two identical MAC addresses, this doesn't normally occur unless you are setting the MAC address manually on more than one location, or you have copied the MAC address from somewhere else. You could try using the one from the NTP test since that obviously works.
Failing that, try moving the Ethernet.begin section to the start of setup before the eeprom code etc.