One can guess that someone who has bought the 4S has restored from a prior device before coming here. Taking that into account, and building on stuff I've read here recently - like EdiMC's shopping list of tweaks (https://discussions.apple.com/thread/3391947?start=10470&tstart=0) and davidch's reset steps (it appears in the current thread very often and it's also archived here along with other stuff - https://discussions.apple.com/thread/3526981?start=0&tstart=0), I've tried to imagine a full circle and more aggressive debug procedure for the new user which builds upon common verifications first, then down to a reset and then to a full reinstall if necessary - something the new buyer can implement rapidly before deciding if the seller's input is required for support or exchange/refund, as time is of the essence. It is just a DRAFT. I claim no credit for the content of the steps, it's just it's slightly aggravating to see the wheel being reinvented all the time... Good luck!
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-="Seeking full value or mitigating the damages for iP4S" procedure=-
I- Pre-reset verifications-
A. Remove all apps from the switcher:
-Press the home button twice and you will see "the switcher" with all the applications in low power state/recently used
-Press on any of them and hold until icons start shaking, once they start moving you will see Red band circle thingy on top left of the application; remove them all
-Remove all opened pages in Safari before exiting if you use it
-Reboot (holding the Home button and Top button down, ignoring the slider, until the phone shut down, wait a couple of minutes, then turn on the phone)
B. If you're still experiencing some drain, check if you have any sim related issues:
-Shut down the phone, remove the sim, start the phone and see if you have any drain - if not, think about trying version 9A406 of 5.0.1 once you reinstall your sim (see http://support.apple.com/kb/TS4148)
C. If you're still experiencing some drain, remove any configured mail account, reboot your phone and reconfigure your email accounts
D. If you're still experiencing some drain, and you're using iCloud or syncing with iTunes, make sure none of your media files(music, video) is incomplete, cut or corrupted - in general pay attention to the integrity of all backed data
If none of these verifications allow you to isolate the issue, try resetting the phone...
II - Reset and options trim (trying to reach a compromise from the full immature feature set - EdiMC's post contains further stuff, see top of post for the link)-
1. Reset all settings (settings app-> general-> reset)
2 a. Go through initial setup steps (lang, wifi, siri, enable location, etc) and choose setup as new phone (don't worry your apps, data, contacts, mail will still be there). Do NOT restore from iCloud or iTunes (It can copy back corrupt settings)
2 b. If you do NOT get the complete new setup screen with language setup and setup as new phone or restore from iTune/iCloud backup, be sure to go back to #1 and reset all settings again (it should happen the second time)
3. In Settings>Location services>System Services ... Disable Setting Time zone, location based iAds, Diagnostic & Usage
4. Set emails and calendars to fetch 30 mins or manual
5. In restrictions set Ping to OFF
6. Disable Automatic Downloads in your App Store setting
7. Set Siri raise-to-speak to OFF and reboot
8. Remove iCloud, then reset network settings (?? will this form of reset undo any of the prior settings)
9. Reduce screen brightness to 40% and turn off bluetooth if you don't use it
10. Fully discharge battery (till it shuts off with the spinning wheel)
11. Fully recharge battery (overnight if possible)
12. Use your phone from full charge to shutoff and take note of your usage time and activities as the battery meter may not be linear and accurate
If you're still experiencing some drain after some time, repeat this procedure down the road or if the reset didn't solve your issue and symptoms reappear immediately, try a fresh reinstall of the OS - note that all your device content will be erased...
III - Reinstall iOS and setup as new-
1. Plug your iPhone to PC/Mac and launch iTunes 10.5.1 or the latest current version for your platform
2. Click Restore. It will automatically initiate a download of iOS 5.0.1 ipsw for iPhone 4S. Wait for the whole process to finish, ie. download, restore software/firmware.
3. Setup your phone as new without using your old restore, download updated apps from the handset and sync your media from your PC/Mac
4. Implement steps 3-12 of part II
If you still experience issues with your rebuilt from scratch handset, seek support from your seller/Apple and ask for a replacement unit or a refund - or take your chance and wait for the next iOS release.
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