I have what seems to be the same problem. I get intermittent connections via my LAN with Mac Pro 4,1 Quad processor. The problem occurs on both ethernet ports, and through wifi. No other computer in the house (including smartphones, etc via wifi and connected computers, Roku, etc.) have this problem. It makes the Mac Pro essentially unusable. I have been able to resolve it (or it just did over time) through hours of "change one thing, retry" including choosing assist in the Network settings. If I choose diagnose or whatever, the last two dots (ISP, Internet?) are always yellow and the test always fails. If I choose configure (under assist - sorry, I can't see it, on a Win machine) the OS seems to turn on all of the connections and try. Sometimes it will make some change and connection will happen, but this is so unreliable, I dont' usually bother, usually fails (which then offers more Dx which are not available, apparently, it just exits the helper).
I've tried rebooting the router, etc, no changes. I've also rebooted the modem, no change. Comcast cable. There may be some error messsages somewhere, but I'm not familiar enough with the massive amounts of reports so don't know where to look. As far as I can tell, this problem didn't happen in this way (only the Mac Pro) until Yosemite. Currently on 10.10.1. Additionally, likely unrelated, I could not take the latest iTunes update, it would show installed but actually fail. Finally, after dozens of attempts including applying update from Apple directly, I deleted iTunes and then re-installed and that apparently solved the problem.
Note I also have Airport, which I cannot manage via my Mac anymore. I'm never attempt to connect to or through it, and manage it through a Win machine (not support in Mac OS for a while, which is maddening). I'm not connecting through it's LAN or Wifi connections, it's dedicated to use by airtunes. Without a standard Web-based management tool, I couldn't imagine ever buying any Airport in the future.
I mention the last two items only for environmental references, I don't suspect they are involved, but thought I should mention. One other item, my MAC Ethernet 0 port MAC is the MAC I have copied into my main router which connects to the Comcast modem. A computer MAC is required by Comcast, which they use as a key to validating the connection, I believe. This has never changed, and note the only the Mac Pro is affected. All of the rest of my LAN is up and running and has solid interent access.
I have, of course, rebooted the machine several times. I'm out of ideas, please help.