How to get video output through HDMI on 18.04? [Intel HD Graphics card]

In short: my laptop doesn't recognize any HDMI output since I installed Ubuntu 18.04.

I am certain the monitor, the cable and my laptop hardware work well, and my one and only graphic card is the integrated Intel HD Graphics. I have rebooted, updated everything and exhausted all the options I could think of.

Description of the problem:

When I plug in the cable, either on a TV or a standard monitor, the laptop does not react and no option shows in the Display system settings. The monitors screens remain black, with only the message "no Source". The HDMI output was working fine with a previous version of Ubuntu on this very laptop, but I can't get it to work anymore, even with a Live USB with a different Ubuntu version (see below).

System info:

• Laptop model: Dell latitude E7470
• Release: Ubuntu 18.04 (bionic)
• Gnome: 3.28.2
• Kernel: 4.15.0-96-generic
• VGA compatible controller: Intel Corporation Skylake GT2 [HD Graphics 520] (rev 07) (this is the only graphic card there is on this computer)

xrandr command output:

julien@julien-Latitude-E7470:~$ xrandr
Screen 0: minimum 320 x 200, current 2560 x 1440, maximum 8192 x 8192
eDP-1 connected primary 2560x1440+0+0 (normal left inverted right x axis y axis) 309mm x 174mm
   2560x1440     60.05 +  59.99    59.99*   59.96    59.95    48.04  
   [...]
HDMI-1 disconnected (normal left inverted right x axis y axis)
DP-1 disconnected (normal left inverted right x axis y axis)
HDMI-2 disconnected (normal left inverted right x axis y axis)

That output does not change once the HDMI cable is plugged in.

Output of lshw command:

julien@julien-Latitude-E7470:~$ sudo lshw -C video
  *-display                 
       description: VGA compatible controller
       produit: Skylake GT2 [HD Graphics 520]
       fabriquant: Intel Corporation
       identifiant matériel: 2
       information bus: pci@0000:00:02.0
       version: 07
       bits: 64 bits
       horloge: 33MHz
       fonctionnalités: pciexpress msi pm vga_controller bus_master cap_list rom
       configuration: driver=i915 latency=0
       ressources: irq:130 mémoire:e0000000-e0ffffff mémoire:d0000000-dfffffff portE/S:f000(taille=64) mémoire:c0000-dffff

Things I have tried:

• Plug into a VGA monitor with an HDMI adapter.
• Plug in the HDMI cable when both the TV and the computer are on.
• Restart the computer with the HDMI cable plugged in and the monitor on.
• Plug in the HDMI cable into my computer (nothing happens on the monitor), then into another computer (the monitor displays computer #2), then back into my computer (monitor screen goes black again).
• Restore BIOS settings to default.
• Use a live USB with Linux Mint 19.3
• Use a live USB with Ubuntu 16.04

The result stays the same: nothing happens on my computer, and the monitor's screen stays black, with a message "no Source".

Do you have any ideas? After some extensive search (on this forum and beyond), I have read that it might be a drivers problem, but I also read that Ubuntu had all the appropriate drivers for Intel HD Grpahics cards natively.

Thanks a lot. Please tell me if I should try some things or give additional information.