That helps narrow things down. It sounds like the downloading of the avatars is what's failing in the first place. We use cURL to download the file from the social networks. There's a few settings for cURL that could cause the avatar not to be downloaded. Things like following redirects, downloading files in general, using https to download content and more could be causing issues.
Another possibility is the Windows filesystem in general. We use the following command to store the saved file to the filesystem:
JFile::write($this->getAvatarPath() . '/' . $tmpImgName, $data);
The '/' is a standard way to separate file paths and should work under most WAMP configurations, but sometimes the '\' is required to not cause problems.
Did you try with the Debug Setting enabled? If so, were there any messages shown on the screen after trying to authenticate or login?
We'll gladly help you get things going on your local test system. I know, in another thread, you mentioned that you'd be trying to get Google+ setup on a real hosting server. This may be another thing worth testing in a real environment as well when you do, just in case.
Let me know how you'd like to proceed on diagnosing the XAMP site and we'll gladly help however we can.
Thanks,
Alex