It appears this phone could have several problems. Do you know the history of the device (was it dropped, water damaged, bent, previous repair attempt, run over by a car ;>)?
The DFU issue could be caused by bad cables or issues with the computer. However, considering you also have a display problem leads me to believe you have logic board issues. Right now you have too many variables.
- Have you tried genuine Lightning cables, rebooted your computer, updated iTunes etc.?
- If you can confirm that the multiple replacement screens are known-good (they work in other devices), then let's eliminate that.
- Try running the phone with the bare minimum...only the battery & dock connected to the logic board. Does the DFU process work now? If not, then try a known-good dock. Don't forget to try a new battery as the 6S has battery issues. If it still fails, then most likely a logic board issue.
- Do a good visual inspection, preferably with magnification of the board, especially around the connectors. Look for missing or partially dislodged components, conductive debris, liquid damage or prior repair errors (poking, scratched traces etc).
Let us know what you find.