Ubuntu won't play videos on either browser or native client

I have a standard Ubuntu 16.04 laptop (recent install), which just won't play videos at all. If I went on youtube, the video would load, and I can jump from various places in the timeline and see the frames, but the video just won't play. No errors in the console. I then look for examples of html5 <video> elements, and I notice that I can't play any of them either. Then I try flash videos, like this one, which loads and I starts only for a couple of seconds, but then stops and does nothing, not even allow me to go back in frames that were played and play them again. Just jump from point in time to point in time and see the individual frame. Again, no errors in console or network. Or this other flash video, which works all the way through and I can replay it.

This happens on both chrome and firefox.

A weird aspect, is that it seems to allow me to play a few seconds on youtube after I reboot, and then stops, as if there was something that got "saturated".

I then tried installing a couple of native mp4 viewers, just to see if I could watch videos that way, but still nothing. One of them is the default ubuntu video tool, and the other is gnome mpv.

I'm slightly confused on what do I try next other than random packages.

It's also worth mentioning that I'm using i3 rather than unity-based technology

EDIT

output of lspci:

00:00.0 Host bridge: Intel Corporation Atom Processor Z36xxx/Z37xxx Series SoC Transaction Register (rev 0e)
00:02.0 VGA compatible controller: Intel Corporation Atom Processor Z36xxx/Z37xxx Series Graphics & Display (rev 0e)
00:13.0 SATA controller: Intel Corporation Atom Processor E3800 Series SATA AHCI Controller (rev 0e)
00:14.0 USB controller: Intel Corporation Atom Processor Z36xxx/Z37xxx, Celeron N2000 Series USB xHCI (rev 0e)
00:1a.0 Encryption controller: Intel Corporation Atom Processor Z36xxx/Z37xxx Series Trusted Execution Engine (rev 0e)
00:1b.0 Audio device: Intel Corporation Atom Processor Z36xxx/Z37xxx Series High Definition Audio Controller (rev 0e)
00:1c.0 PCI bridge: Intel Corporation Atom Processor E3800 Series PCI Express Root Port 1 (rev 0e)
00:1c.1 PCI bridge: Intel Corporation Atom Processor E3800 Series PCI Express Root Port 2 (rev 0e)
00:1c.2 PCI bridge: Intel Corporation Atom Processor E3800 Series PCI Express Root Port 3 (rev 0e)
00:1f.0 ISA bridge: Intel Corporation Atom Processor Z36xxx/Z37xxx Series Power Control Unit (rev 0e)
00:1f.3 SMBus: Intel Corporation Atom Processor E3800 Series SMBus Controller (rev 0e)
01:00.0 Network controller: Broadcom Corporation BCM43142 802.11b/g/n (rev 01)
02:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8101/2/6E PCI Express Fast/Gigabit Ethernet controller (rev 07)
03:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS5229 PCI Express Card Reader (rev 01)