iMac slow to connect to internet over ethernet

I have the lastest iMac 27" with Moutain Lion. After connecting wirelessly to my Time Capsule, I decided to use an ethernet cable instead. I expected it to be faster and more reliable.

I don't notice any real differences in transfer speeds. But I do notice it takes much longer to establish a connection after waking from sleep. With Wifi it took only a few seconds, and with ethernet it takes at least 20 seconds to go online. Why is that? My router is set to DHCP (all default settings)

I have disabled Wifi on my iMac, and I have put Ethernet first in the list of networks in System Preferences.

Also, why is it disconnecting completely? I'm interested in Wake-On-Lan to remotely wake my iMac, but that doesn't work either. Maybe it's related?

Annybody any suggestions?