I'm sorry if this isn't the right place to post this (I found this page via google) but I've got the same message appearing when trying to authorize the first Mass Effect game, on Windows 7 64 bit, the 'there is a problem connecting to the server.' message specifically. Installed it yesterday, and when I click play, after a pause it throws up that message. Disk install, the old 5 authorization limit for DRM, no Origin or Steam involved. I de-authorized my install on my old operating system last week, using the de-authorization tool and it was fine. While trying to figure out what was going wrong yesterday, I tried using that, and it got the same 'problem connecting to the server' message a few times, before working. I've been poking at it since then, and it alternates between working and throwing up the error message.
IF this is a related issue (which I'm hazarding a guess it is, considering the timing and it being the same message) it's on EA's end, not operating system. To double check that, this morning I plugged in a hard drive with Windows XP, where Mass Effect has worked perfectly for years now. The install there had been de-authorized, so it'd need a re-authorize to work, and it didn't. Again, same message about there being a problem connecting to the server. So whatever it is, it's not on the computer's end.
(Again, sorry if this isn't the place to post this and there's no chance of the problems being related, but I thought I'd chip in when this is the only place I've seen the issue mentioned. Been too anxious to make my own post about it on the Mass Effect help forum.)