Oddly, this is not working for me. I can log into the ShopRunner site without any problem, but when I try to sign in from the shopping cart of Newegg, it tells me that the credentials are wrong. I've checked and re-checked to be sure they are the same I use on the ShopRunner site proper and I can't work it out. I've tried on EMS.com as well with no luck. It's very strange.
I sent a message to ShopRunner's tech support, so we'll see how that goes.
To follow up with my experience with ShopRunner's tech support:
I sent them a detailed e-mail describing the problem above and they responded by saying I might be using the merchant credentials (even though I clearly stated I wasn't) and suggested I call their phone support.
I called their phone support today and wow, I don't think I've ever dealt with more inept tech support. On the bright side, I got an agent quickly who was a native speaker of English. But it was all downhill from there. I described the problem and she had to put me on hold for five minutes to ask a supervisor what to do. She then came back saying that I had to set up a separate log-in for each merchant. This made no sense to me and I asked her how to do it, but it became clear that she was talking about the account with the merchant itself, which I have already. So again she had to go back to her supervisor. When she finally came back she said she would have to open a ticket for me. Fine. She asks for my e-mail address for the account and I give it to her. She seems confused because it isn't a yahoo or AOL address. I try to explain that I own my own domain name and that the e-mail I've given her is valid and is the one associated with my account. She then tells me that she doesn't need a domain name, she needs an e-mail, "something ending in @yahoo.com or similar". Oy. She then asks for a phone number for the account. I don't think I have one entered into my account information, so giving her that information doesn't go anywhere either. Eventually, using my name, she's able to find my account and form the support ticket. And she tells me it will take 2-3 business days and that they'll call me. I ask for an e-mail notification instead and here we go again ... I guess I should have known better.
tl;dr version: ShopRunner is a nice service, but woe betide you if you ever need tech support.