I doubt that it is due to permissions problems. The message says "timeout" and this indicates a connection problem. It could mean that the server/repository you are trying to use is simply down (that happens). But it also could be due to a proxy or a VPN-tunnel (I can't install packages on my work PC when I'm connected to our intranet).
Try to install the pgf-package directly with the package manager. Try different repositories (menu repository). If both doesn't work: Get from CTAN the files
and perhaps other package from systems/win32/miktex/tm/packages/. Put them all in an empty folder outside your miktex. Then use the package manager to install them by using the folder as "local repository".