I'm running Fallout 2 on a Windows XP SP3 laptop with Intel "Extreme" (82852/82855 GM/GME series) graphics, and I'm experiencing problems that mean I simply can't play the game.
The intro movies (the Interplay logo, Black Isle logo and longer intro movie) all play fine, but when the long intro movie finishes, the last frame of the movie stays on screen but with corrupted colours, and nothing else happens - I assume there's supposed to be a menu or something here. Pressing Escape quits back to the desktop.
I've tried running in Win95 compatibility mode, and forcing to 640x480, and 256 colours, and nothing seems to help.

Can you post a DXdiag for us ??Maybe there is something in there that may need rectifying.
Turn off any antivirus software when running the game. Also, you shouldn't have to run this game in any sort of compatibility mode. The GOG installer should take care of that for you.

Okay, just run DXDiag, and it fails on creating a DX7 surface (DX8 and 9 are fine).
The full log is at http://www.parm.net/DxDiag.txt
I'll give it a go with AVG turned off in a second...

Here's one problem:
Display Devices
---------------
Card name: Intel(R) 82852/82855 GM/GME Graphics Controller-0
Manufacturer: Intel Corporation
Chip type: Intel(R) 82852/82855 GM/GME Chip
DAC type: Internal
Device Key: Enum\PCI\VEN_8086&DEV_3582&SUBSYS_FF001179&REV_01
Display Memory: n/a
Current Mode: 1024 x 768 (32 bit) (60Hz)
Monitor: Digital Flat Panel (1024x768)
Monitor Max Res:
Driver Name: ialmrnt5.dll
Driver Version: 6.13.0001.3413 (English)
DDI Version: 8
Driver Attributes: Final Retail
Driver Date/Size: 12/30/2002 12:21:40, 33792 bytes
WHQL Logo'd: Yes
WHQL Date Stamp: n/a
VDD: n/a
Mini VDD: ialmnt5.sys
Mini VDD Date: 12/30/2002 12:20:06, 87579 bytes
Device Identifier: {D7B78E66-76C2-11CF-9C7F-01DFA3C2CB35}
Vendor ID: 0x8086
Device ID: 0x3582
SubSys ID: 0xFF001179
Revision ID: 0x0001
Revision ID: 0x0001
Video Accel:
Deinterlace Caps: n/a
Registry: OK
DDraw Status: Not Available
D3D Status: Enabled
AGP Status: Not Available
DDraw Test Result: Not run
D3D7 Test Result: Failure at step 8 (Creating 3D Device): HRESULT = 0x8007000e (Out of memory)
D3D8 Test Result: All tests were successful.
D3D9 Test Result: All tests were successful.
Description: Avance AC97 Audio
Default Sound Playback: Yes
Default Voice Playback: Yes
Hardware ID: PCI\VEN_8086&DEV_24C5&SUBSYS_FF001179&REV_03
Manufacturer ID: 1
Product ID: 100
Type: WDM
Driver Name: ALCXWDM.SYS
Driver Version: 5.10.0000.4010 (English)
Driver Attributes: Final Retail
WHQL Logo'd: Yes
Date and Size: 9/16/2002 19:25:02, 941516 bytes
Other Files:
Driver Provider: Avance Logic, Inc.
HW Accel Level: Full
Cap Flags: 0xF5F
Min/Max Sample Rate: 100, 100000
Static/Strm HW Mix Bufs: 33, 32
Static/Strm HW 3D Bufs: 33, 32
HW Memory: 0
Voice Management: No
EAX(tm) 2.0 Listen/Src: Yes, Yes
I3DL2(tm) Listen/Src: Yes, Yes
Sensaura(tm) ZoomFX(tm): No
Registry: OK
Sound Test Result: All tests were successful.
Your graphics driver is over 6 years old. Try updating your graphics drivers (and your sound as well because they too are over 6 years old).
Go here and there should be a download for the Intel chip ID utility use that and download the drivers required. See if that helps.

The Intel driver refuses to install, and insists I use a driver from my computers manufacturer, which in this case it Toshiba. The driver installed is the latest one Toshiba offer, and it works fine for everything else I've ever tried (that I would expect to run on 6-year old hardware, natch), up to and including World of Warcraft and Half Life 2 (albeit painfully slowly)

How in the world does that refuse to install?? Did you pick the wrong one by chance? Just trying eliminate possibilities here, not trying to say you're an idiot.

It pops up a little dialogue box saying "Cannot install on this machine", and tells me to contact my manufacturer. It's very definitely the right driver, and I've tried both the self-extracting .exe vesion and the .zipped version, and they both give the same result. It's not an uncommon thing for laptop vendors to have custom IDs for their otherwise standard off-the-shelf hardware, so they can control delivery of drivers and so forth - Dell do it all the time, so (for example), generic NVidia drivers won't install on a Dell laptop with an NVidia graphics chipset. It's very annoying, but very common.
(indeed, it's something we see - and spend quite a lot of time dealing with - at work; I'm a s/w eng for a small chip design company, and when we sell our chips to third-party OEMs, they all want it "branding" as their own solution, even though it's the same damned hardware in all the devices being driven by what is 99% identical software also)

That is quite odd because my manufacturer's (Gateway) drivers are older than the Intel ones so I used Intel's site with no problem. I would try going on your manufacturer's website, I guess, and try to get the most recent drivers from there. I know you probably know this and all. The only reason I am harping on the drivers is because of their age...
I know you're on XP, but in the compatibility menu have you tried checking the box that says "Disable Visual Themes"? I am not sure if XP has that as it has been a while since I used XP.
Also, try setting your desktop resolution to 800*600.
Try the solutions listed in this thread. People have reported some measure of success.
http://www.gog.com/en/forum/Fallout_Series/fallout_2_colors_problem

The driver installed is the latest one Toshiba offer
Yes, I've tried it, but it doesn't work - it's highly unlikey that it would have done anything, anyway, as it's related to theming on common controls in Win32 desktop applications.
Doesn't help.
That seems to relate to Vista primarily, but I'll investigate. It doesn't seem, though, to be just a "colours" problem - I get the last frame of the video, and then nothing else - it just stays on the screen, and all I can do is press escape to quit.
edit: I've gone through that thread and tried everything suggested - the high-res patch makes it crash out with a DX error - I'm guessing because it needs shaders and my card can't provide them, and nothing else makes any difference at all...

You may be right on the shaders. Perhaps tech support will know more because I am out of ideas. Sorry I couldn't help you though.

Ok a couple things you could try to get it working, you could try turning hardware acceleration on or off you can do this by going to Desktop --> Properties --> Settings --> Advanced --> Troubleshoot and changing the slider.
You could also try disabling your videocard and seeing if it works without it. I've never done this with an intel extreme graphics card so if you are not sure or know that if you disable your graphics card that you wont beable to see anything don't do this. You can do this by going right clicking my computer going to properties -->Hardware --> device manager find your card in the list and click the disable button along the top bar. Its probably under display adapters. Restart your computer and see if it runs with the card disabled.
If neither of those work you could try http://www.nynaeve.net/?p=52 It tricks games into running in a window that require full screen normally. I've never used this myself but a friend told me about it, so use this at your own risk.

I've just tried this on another machine - a Samsung NC10 netbook - and got exactly the same problem. I've emailed Support and attached the DxDiag.