Q: iphone 4s back up failed, update failed phone stuck on logo

Back up to itunes and icloud failed, update to 9.2.1 failed phone is now stuck on apple logo

I am looking for some assistance, my iphone 4s started playing up on 11/02/16 - I noticed that it was deleting apps from phone and then they would reappear. One of my apps would not open at all so i decided to uninstall it ans reinstall but it would not down load.  I kept trying but nothing would happen as it was getting late I decided to leave overnight.

12/02/16  - i decided to back up phone to itunes - My phone was recognised in itunes, but not recognised in my computer.  I tried to back up over itunes it failed it kept saying I needed to transfer purchases and then itunes would state that it couldnt transfer and fail.

so i went into phone and changed my photos to on in icloud and asked it to back up now, this also failed,  I tried several more times on both itunes and icloud and it would not back up.

As it needed an update to 9.2.1 I decided to try this but the update would not work either.

I decided to restart phone and I got the connect to itunes logo so I decided to try on my sons laptop (as this was newer) and it said update or restore so i have been trying to update but it fails every time usually with error code 27.

I do not want to restore as I have got a lot of photos of my new born son on there and do not want to lose them,  I understand you should back up and that is exactly what I was trying to do!!! I had got behind with backing up because he is so young,   I do not care about anything else on the phone but those photos.

now my phone is stuck with just the apple logo which goes off after a minute or so.

Please any advice welcome but no lectures on backing up.  Thank you