Android studio is stuck on Gradle: Initalise build. Running as administrator and I've let it through my firewall.

Are you able to run Gradle (gradlew) commands via the command line? You mentioned letting it through your firewall -- does that mean that normally things like Gradle (and Studio) would not have direct access to the net from your environment? Did you open the firewall hole before or after you started the stuck operation?

But, the question is: independent of Android Studio, are you able to use ./gradlew from a terminal window at all? That is, do you have sufficient network access, JAVA_HOME set, and related environmental configuration to ensure that the self-loading Gradle system will work at all? Or is your environment so jacked that even this won't work? I don't believe you've said what OS you're on, which in these cases is important to disclose (both type, and version).

For example, if you are on Linux, the hang could be caused by some operation trying to retrieve random numbers from /dev/random and the entropy gathering daemon is out of entropy, causing blocking until more entropy is produced. But, without knowing the OS, it's harder to isolate what might be the cause.

What would happen if you simply killed Android Studio and tried starting again? It's not likely that it will get "unstuck" on its own at this point...

Hmmm....have any virus scanners that might be interfering with this working? Does Windows 8.1 have the annoying property that older versions of Windows had where some important (and modal) alert dialogs don't pop up over other windows so you don't know they are there?

Since Android Studio is basically IntelliJ Idea with some augmentation, what would happen if you installed the community version of Idea with the Gradle plugin and see if you can spin up a simple Java project that way, just to verify that your environment isn't somehow preventing any IJ from working properly?

Gradle (well, really Maven) will download any dependencies it needs, which for Studio, could be considerable. Is it possible that where these dependencies are trying to go in your file system is somehow write-protected or otherwise preventing the retrieval of the necessary files?

What about my earlier question about ./gradlew from the command line? Tried that yet as a way see if the problem is specific to Studio, or is endemic to your environment?

Ah. That sort of administrative level restriction is important to disclose when describing a problem as it materially affects the set of potential causative factors and therefore the course of diagnosis. . This likely is a problem you will need your local administrators to help you with.