Personally I think the best way to do this would be to set up a build server (or continuous integration server) such as hudson or teamcity. You could then edit your code in a web editor (or simply a more lightweight editor) and just commit and push it to the build server. The build server then does all the heavy lifting and tells you if the build/passed or failed. It can even be set up to run your unit tests!
You might want to reference this question in regards to tips on how to set this up. If you use Github you get the added bonus of being able to use Ace to edit files - though I would suggest using a more robust editor and pushing your repository up manually.
If you are really keen on building on the internet you can check out compilr which sounds like what you really want (though I wouldn't recommend it - you really need you own build flow!)**.
** does not imply that the compilr service is not a good one