Kernel panics and warnings with Intel Core 2 Duo T5870 and GME965

During the boot sequence we see a stack trace (check the dmesg), and after some time using the computer, the kernel panics and everything hangs (see attached pic).

I've tried the 32 bit version of the following kernels:
linux-image-4.4.52-040452-generic (downloaded from the kernel ppa)
linux-image-4.8.0-34-generic
linux-image-4.8.0-37-generic
linux-image-4.8.0-39-generic
linux-image-4.10.1-041001-generic (downloaded from the kernel ppa)

I've also tried the 64 bit live version of Ubuntu 16.04.2, plus another old distro with 4.3.2. Same result in all cases.

This issue can be reproduced in another machine with the same specs (same laptop).

Booting with nomodeset makes this problem go away, but the resolution is limited to 1024x768 and it's not a permanent fix, obviously.

By the way, here's the output of lshw -c video (as non-root, since it segfaults as a root)
$ lshw -c video
WARNING: you should run this program as super-user.
  *-display:0
       description: VGA compatible controller
       product: Mobile GME965/GLE960 Integrated Graphics Controller
       vendor: Intel Corporation
       physical id: 2
       bus info: pci@0000:00:02.0
       version: 0c
       width: 64 bits
       clock: 33MHz
       capabilities: vga_controller bus_master cap_list rom
       configuration: driver=i915 latency=0
       resources: irq:30 memory:e8400000-e84fffff memory:d0000000-dfffffff ioport:6000(size=8) memory:c0000-dffff
  *-display:1 UNCLAIMED
       description: Display controller
       product: Mobile GME965/GLE960 Integrated Graphics Controller
       vendor: Intel Corporation
       physical id: 2.1
       bus info: pci@0000:00:02.1
       version: 0c
       width: 64 bits
       clock: 33MHz
       capabilities: bus_master cap_list
       configuration: latency=0
       resources: memory:e8500000-e85fffff
WARNING: output may be incomplete or inaccurate, you should run this program as super-user.

ProblemType: Bug
DistroRelease: Ubuntu 16.10
Package: linux-image-4.8.0-39-generic 4.8.0-39.42
ProcVersionSignature: Ubuntu 4.8.0-39.42-generic 4.8.17
Uname: Linux 4.8.0-39-generic i686
AlsaVersion: Advanced Linux Sound Architecture Driver Version k4.8.0-39-generic.
AplayDevices:
 **** List of PLAYBACK Hardware Devices ****
 card 0: Intel [HDA Intel], device 0: 92HD75B2X5 Analog [92HD75B2X5 Analog]
   Subdevices: 1/1
   Subdevice #0: subdevice #0
ApportVersion: 2.20.3-0ubuntu8.2
Architecture: i386
ArecordDevices:
 **** List of CAPTURE Hardware Devices ****
 card 0: Intel [HDA Intel], device 0: 92HD75B2X5 Analog [92HD75B2X5 Analog]
   Subdevices: 1/1
   Subdevice #0: subdevice #0
AudioDevicesInUse:
 USER PID ACCESS COMMAND
 /dev/snd/controlC0: aulamobil 1494 F.... pulseaudio
Card0.Amixer.info:
 Card hw:0 'Intel'/'HDA Intel at 0xe8604000 irq 32'
   Mixer name : 'IDT 92HD75B2X5'
   Components : 'HDA:111d7608,103c308a,00100202 HDA:11c11040,103c1378,00100200'
   Controls : 25
   Simple ctrls : 12
Date: Wed Mar 1 11:44:40 2017
HibernationDevice: RESUME=UUID=d74ee806-fdc4-4421-904e-3a84e9035047
InstallationDate: Installed on 2017-01-19 (41 days ago)
InstallationMedia: Lubuntu 16.10 "Yakkety Yak" - Release i386 (20161012.1)
MachineType: Hewlett-Packard Compaq 610
ProcEnviron:
 TERM=xterm
 PATH=(custom, no user)
 LANG=ca_ES.UTF-8
 SHELL=/bin/bash
ProcFB: 0 inteldrmfb
ProcKernelCmdLine: BOOT_IMAGE=/boot/vmlinuz-4.8.0-39-generic root=UUID=6531de7d-5d30-4fd7-bc0d-e3ed7dde2cce ro quiet splash vt.handoff=7
PulseList:
 Error: command ['pacmd', 'list'] failed with exit code 1: Home directory not accessible: Permission denied
 No PulseAudio daemon running, or not running as session daemon.
RelatedPackageVersions:
 linux-restricted-modules-4.8.0-39-generic N/A
 linux-backports-modules-4.8.0-39-generic N/A
 linux-firmware 1.161.1
SourcePackage: linux
UpgradeStatus: No upgrade log present (probably fresh install)
dmi.bios.date: 11/20/2009
dmi.bios.vendor: Hewlett-Packard
dmi.bios.version: 68PVU Ver. F.0B
dmi.board.name: 308A
dmi.board.vendor: Hewlett-Packard
dmi.board.version: KBC Version 26.08
dmi.chassis.asset.tag: CNU00268JB
dmi.chassis.type: 10
dmi.chassis.vendor: Hewlett-Packard
dmi.modalias: dmi:bvnHewlett-Packard:bvr68PVUVer.F.0B:bd11/20/2009:svnHewlett-Packard:pnCompaq610:pvrF.0B:rvnHewlett-Packard:rn308A:rvrKBCVersion26.08:cvnHewlett-Packard:ct10:cvr:
dmi.product.name: Compaq 610
dmi.product.version: F.0B
dmi.sys.vendor: Hewlett-Packard