Sounds very similar to my error 53 issue. I swapped out a new LCD Shield plate which had the home button cable and was able to then restore. I assume that's what you also replaced when you are talking about the flex cable? If you have perhaps its related to the home button / Touch ID assembly which can't be replaced to restore the device.
I know this is a dead thread (no pun intended) but I have the same issue. iPhone 5 dead, bought two new batteries thru iFixit, battery worked fine. Then over a week of charge/discharge cycles it finally went dead again when it gets down to 0%. So I chucked the second battery in, battery charged to 100% & since its fully discharged its dead again. Any thoughts guys?
I was given a water damaged iPhone 6, I tried DFU Restoring it and it would error 53 on both my Mac & Windows PC and with different cables & up to date iTunes clients. It had fried itself in the home button cable that continues behind the LCD Shield plate to touch ID/home button assembly connection. I thought I would try getting a new LCD Shield plate that includes the home button cable. I swapped out the LCD Shield plates out and SUCCESS with the DFU Restore! Error 53 in this instance was hardware related! Thanks for the some of the posts here that helped me pinpoint the likely cause which you only discover when trying to restore!