We had a similar issue. Uploaded builds were queueing up and it simply said "Processing" with the popup help, “After builds are uploaded they will go through a processing state before they can be used.” Days passed.
Selecting "Internal Testers," making a change, and saving seemed to immediately clear the queue: The latest build was now active and available for testing. I've done this twice with two different apps now.
Update: At this point, all bets are off. It seems "processing" happens when Apple quietly upgrades iTunes Connect and there's nothing you can do about it.
On September 23, 2015 iTunes Connect didn't accept any uploads for nearly 24 hours. The "Internal Testers" trick didn't work. Eventually bumping the version number (to avoid "duplicate binary" error) and re-submitting worked.
The next day, Surprise! iTunes Connect was completely changed. I guess we were all looking at a dead site while they brought up the new version in the background :(
In our case we can still see dozens of "failed" uploads still sitting in the "processing" state. Oh well.
Some people report using Application Loader works better than Xcode for submitting builds to iTunes Connect. You can find it inside Xcode now, under the Xcode menu "Open Developer Tool" item.
Sometimes this works. Sometimes it doesn't. Your milage may vary ¯\_(ツ)_/¯
Application Loader
to upload my build. It was the only build that finished processing after a 2-3 hours. The rest uploaded with Xcode7 have yet to finish over 12 hours later. – MarkApplication Loader
and they are still processing now 10 hours later. – Mark