Since Jessie's kernel dates back to 2014, we can't expect it to have much support for Intel hardware or other devices, such as wifi, that have been introduced since then. This means Intel fifth-generation or better--i.e., Broadwell, Skylake, or Kaby Lake graphics and support hardware. The code numbers for your processor relate to the generation--so an i5-6500u is sixth-generation Skylake, and -7700 would be seventh-generation Kaby Lake. Symptoms can include no brightness control, wireless interface, touchpad, sound, 3D graphics, ability to suspend the machine, and so on. However, if you can get a wired connection going and at least a terminal interface, there are updated packages available in jessie-backports that should get your machine working well.
First, if you have one of these machines with integrated graphics, forget about using the default GNOME 3 desktop until the graphics are working--try a simpler desktop like xfce or LXDE if you really need a GUI, since these have a chance of working with the crippled graphics that is the best that the stock kernel can provide.
If you manage to have a wired connection, then add the jessie-backports repository*:
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sudo tee -a /etc/apt/sources.list <<< "deb http://httpredir.debian.org/debian jessie-backports main contrib non-free"
*Do all the commands in a root terminal if you did not enable sudo.
Then update the apt package database so the backports will be added to it:
We're going to assume you are running 64-bit on your new hardware--there's little reason to use 32-bit on modern machines--so update the kernel and graphics stack from backports:
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sudo apt-get install --target-release jessie-backports linux-image-amd64 xserver-xorg-video-intel libegl1-mesa libgl1-mesa-glx libgl1-mesa-dri
Sixth and seventh generation Intel graphics require non-free firmware also be installed:
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sudo apt-get install --target-release jessie-backports firmware-misc-nonfree
The new kernel will be added to the GRUB menu and be the default, but the old one will still be available. If you need the 32-bit video packages for something like Wine or Steam, install them after you confirm that the new kernel and video is working after a reboot. This can be seen by installing "inxi" and checking the output of
crippled output will mention gallium and llvmpipe, but a good one will have something similar to
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GLX Renderer: Mesa DRI Intel HD Graphics 520 (Skylake GT2) GLX Version: 3.0 Mesa 13.0.3
Once you see that, the 32-bit packages can be installed if necessary:
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sudo dpkg --add-architecture i386
sudo apt-get update
sudo apt-get install --target-release jessie-backports xserver-xorg-video-intel:i386 libegl1-mesa:i386 libgl1-mesa-glx:i386 libgl1-mesa-dri:i386
Most wifi hardware now requires non-free firmware. A newer kernel's internal wifi drivers often requires matching newer firmware packages from backports, so install what you need in the same command format. For example, Intel wireless chipsets would require
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sudo apt-get install --target-release jessie-backports firmware-iwlwifi
This guide was shamelessly cribbed from
Head on a Stick's original at the BL forums.