So to confirm, you're accessing your email using the Safari web browser, and there is something that is preventing the web mail system from uploading photos from your Mac OS X system to the web mail provider's system, for sending out with your message?
If so, this is an issue centrally involving whichever web mail provider you are working with, and probably problems with their web mail system. That would be fairly unusual, but not impossible.
If Geek Squad was looking at Apple's Mail.app tool and not at Safari (and if you're accessing your mail via Safari and a web interface), then the Geek Squad folks were either headed off in an unexpected direction, or they were looking to provide you with a different path into your mail provider; a path that did not involve the web mail interface, and that used Apple Mail.app to access your mail.
Please provide your OS X or iOS version, and the identity of the web mail provider. It might also help to post the exact text of the error message, if there's something more than "unable to attach files".
Also, have you tried attaching exactly one (small) photo to a message?