I am just another victim of this IOS 9 glitch after attempting to upgrade via wifi. After several attempts at troubleshooting the frozen phone, I got it to work. Here is what I did for my son's iPhone 5S. If your phone is stuck or frozen in any way while attempting to upgrade to IOS 9, try this:
1. Go to computer & open iTunes; do not connect phone yet, but be ready to connect
2. Update iTunes on your computer to 12.3 before proceeding; IOS 9 will NOT work with previous versions of iTunes so you must update before moving forward. If you cannot update, please follow these steps without doing so, and then choose to restore your phone from latest backup.
3. Hard reset your iPhone by pressing & holding the HOME & POWER buttons at the same time, and hold them down while the phone reboots
4. When the apple symbol reappears, immediately let go of the HOME & POWER buttons for a split second & press them both again simultaneously & hold them down
5. At this point, my phone entered the restore mode.
6. Plug your iPhone into your computer with iTunes already open (and updated to 12.3 if possible). iTunes immediately recognized the phone (which it had not while it was stuck in "slide to download" mode)
7. iTunes (via the computer) prompted me to either download IOS 9, or restore the phone using the latest backup. At this point you have 2 options.
A. If you want to abandon the upgrade, go ahead & restore your phone USING THE LATEST BACKUP from your computer. I did not do this, so hopefully it will work and you will be back in business with whatever IOS version you had before. Once complete, you should be finished here if this is what you choose. WARNING: If you do not use the latest backup to restore, you will be restored to factory settings & will lose all data & apps including photos, contacts, etc. Be careful not to choose the wrong restore options!!! If you are not sure, call Apple Support.
B. I chose to download IOS 9.
8. iTunes immediately began downloading IOS 9. The phone continued to have the restore symbol showing on its screen for several minutes, then it showed the Apple symbol with the download bar beneath it. iTunes showed the download activity simultaneously. Be patient, it may take a while, mine was about 15 minutes.
9. Once the phone & computer have upgraded to IOS 9, you should see the option on your phone again to slide...do so, unlock your phone if requested, and then the phone should go through a series of questions (mine was click continue, choose your wifi network from the list showing, continue again, and then finish). Your questions may be different depending on your phone & network settings.
10. Phone may then show Apple symbol again, and should work using IOS 9 now.
This worked for me. However, if the download brings you back to the frozen iPhone screen once again, you may want to choose option 7A above which is to go back through the steps and then restore your phone from its latest backup rather than continue with attempting to upgrade to IOS 9. Maybe best to wait until they get the bugs worked out! At least if you can get it to restore using latest backup,
Good luck everyone. Cheers!