I asked a question over here about the best way to go about meeting a prospective PhD advisor (Prof X). It was mostly agreed that I should ask my current advisor (who knows Prof X) to introduce me. I did ask him, and he responded by saying that he is happy to introduce me, so all well and good. However about eight days or so have passed since then and I haven't heard from him despite a couple of spaced out follow up emails. No answer to my calls either. What can or should I do at this point? Should I go back to my original plan of directly trying to contact Professor X? This is a bit frustrating, since in the meantime other grad schools are finalizing and mailing out their decisions and this school is my top choice. Thanks for any suggestions.
The situation doesn't sound promising, but don't lose hope just yet. As C is your advisor and you are nearing completion, you would hopefully have some kind of relationship with him, that if, for example, there were an informal discussion with X and he had changed his mind about offering support, then something might gently have been communicated to you from C to dissuade you from pursuing X.
As to how to proceed, also in reference to the discussion to your previous question, C is likely going to be your best way in. I'm not sure what "spaced out emails" entails, exactly, but if no joy is to be had from email or phone, try visiting. A person physically there is much harder to ignore than not picking up a phone or answering an email. You may get a sense of whether what's happened in paragraph 1 is the case.
In the unfortunate event that C no longer wishes to support, of course you can go with your original plan, but it would be best (as was also previously mentioned) to remove reference to C from any correspondence, as the mention of the name implies some kind of endorsement (or is just name-dropping, which may also be looked on unkindly), and try your luck. It may be a long shot, if X is that big, but if the in-person attempt to bring C on-board doesn't work, no one can be forced to do anything he doesn't want to do. Just suggestions, borrowing from some personal experience, hopefully helpful. Good luck.