ITunes wont recognise iPhone

Question

iPhone 5s model A1457.
I have two Windows 7 64 bit laptops, one has iTunes 11.4 running, the other has the latest iTunes 12.0.1
iOS was 7.something and I stupidly tried to update overthe air to 8.1.2
Something went wrong and it is stuck in recovery mode.
Recovery screen (iTunes logo + cable picture) lasts only for a couple seconds before it turns off.
Cable seems to work because it worked for other iPhones I have used.
If I open iTunes, connect the cable to my laptop, then connect the other end to my phone, the phone turns on and then goes to the recovery screen.
iTunes does not recognise the phone.
Since I cannot do anything else with the phone, it will turn back off in a couple seconds.
Already reinstalled itunes the proper way (uninstall programs in order - restarted laptop - reinstalled)
Checked device manager. I believe the phone should appear under "portable devices" or something but "portable devices does not appear in device manager.
Also, I believe there is supposed to be something under "Universal Serial Bus controllers", but I can't see anything related to the phone.
Tried using different USB ports, but that doesn't work. (also note: unplugging the cable from the phone all turns it on and shows the recovery screen for several seconds before turning off)
Did something that involved turning off itunes, disabling then enabling apple mobile support (or something like that), then turning iTunes back one - didn't work

Answer 1

I somehow managed to fix it.
Solution:
It seems that iTunes could only recognise my phone if I plugged it in a certain way.
With the phone in one hand, I used my other hand to hold the cable (with thumb+ side of index finger) just under the head of the usb end.I then pushed the cable in (towards the phone). Without bending the cable, I slowly adjusted my hand till it worked. I knew this worked because I heard the notification sound from my pc.
This wasn't an issue of getting the right cable because I have used other cables which worked on other phones but not mine (this leads me to believe the port (hole) of my phone is slightly deeper than usual. that said i usually dont have this problem of needing to push the cable in to get it to work. I do however have a problem of getting cables that work (which could be relevant). My trusty one (which isnt actually trusty) works if i move it about and orientate it in a way that it works i.e. its very tempermental
well anyway....
Knowing all this, I held the phone in my armpit (to free up a hand), and again reoriented the hand holding the usb cable while pushing in towards the phone such that it worked (heard the notification sound from my laptop). with my other hand I started the process of restoring the ios on the pc.
NOW I HAD TO BE CAREFUL. If I moved out of position (even a little bit) the phone would disconnect and the restore would fail, so I had to painstakingly stay in position for the whole restore process. It took about 4 attempts but I succeeded in the end. You should watch out, even if itunes is still "extracting" the ios file my phone could still disconnect (i would only know if it disconnected when i get a failure message after it finishes extracting). i had to hold still throughout the extracting, the iphone checks, the actual iphone restoring process (where you see the loading bar on the phone) etc. after the extracting period, the notification sounds my pc makes when i plug something in went off occasionally which worried me, but i still kept still and in position throughout till i succeeded. so you cant necessarily trust the sounds completely
The restoring my backup process was not as painstaking. I plugged everything in, wiggled the cable a little till i could see my phone in itunes, then just restored the backup easily.
my hand aches from holding the cable for so long but i have succeeded in the end. I don't believe I have ever seen advice like what I have mentioned on the internet so i hope this will help everyone who seem to have tried everything without success