I've already sent a query to tech support on the matter. It read thus:
"When I try to run the Sacrifice executable, I'm first prompted to choose a display driver/API. The game then switches to full screen with an all black background, and I can glimpse a couple of lines of white text near the top of the screen, before my computer reboots by itself."
They've given me a couple of suggestions which haven't worked, so I thought I'd ask to see if anyone here has a clue, while I wait for tech support to respond again.
If anyone has any ideas, I'd appreciate it.
(PS: I've already tried resizing the page file. It didn't work.)

Try to run it in forced windowed mode with D3DWindower and see if it behaves differently:
http://generaladmission.home.comcast.net/files/D3DWindower.zip
What suggestions have not worked?
What are your system specs?
What other software is running in the background?

http://generaladmission.home.comcast.net/files/D3DWindower.zip[/quote[/url]]
Thanks for the tip. I managed to get the game to run in windowed mode, but it still rebooted.
- Reinstalling the game.
- Running in compatibility mode - in this case my computer doesn't reboot, I simply get an error message and nothing else happens.
- Disabling vsync in my card's D3D-settings (suggested by GoG tech support).
- Editing certain fields in Sacrifice's "option" key in the Windows directory (also suggested by GoG tech support). In this case the fields didn't exist in my registry. I suspect Sacrifice crashes before it can even create an initial configuration for itself.
- Limiting the size of my page file to 512 MB.
- Disabling antivirus and antispyware software.
I've also tried running the demo to see if it behaved differently. It shows the same black screen with white text, then a splash screen for Shiny, and then reboots.
Windows XP SP3
AMD Athlon XP @ 1.8 GHz
1 GB RAM
ATI Radeon X1650 pro w/512 MB RAM (AGP)
Soundblaster Audigy 2
I also usually keep my page file size at 2.5 GB.
-Windows Live Messenger
-ATI Tray Tools
-Spybot Search & Destroy
-AVG Antivirus
-MBprobe
-DAEMON virtual drives
-Some processes related to my MP3 player and it's software (Creative Zen).

At this point I can only offer guesses and suggestions in an attempt to narrow the field of variables. It's up to you if you want to try them.
First off, I have no first-hand experience with SP3 or ATI cards/drivers, so I don't have much to offer. Have you looked into some of the other SP3-related issue, such as the reboot issue here:
http://msinfluentials.com/blogs/jesper/archive/2008/05/08/does-your-amd-based-computer-boot-after-installing-xp-sp3.aspx
Do you know if windows is set to automatically reboot upon system failure? Check here:
Control Panel->System->Advanced tab->Startup & Recovery Settings->checckbox for 'Automatically restart'
Try killing all the background processes you mentioned (not just disabling). Use Task Manager if you have to. None of them are essential, and a single test-run with all of them terminated will give you a good indication if any of them are the culprit. If you are concerned about being vulnerable with avg/spybot closed, just disconnect from the internet while you test.
"Running in compatibility mode - in this case my computer doesn't reboot, I simply get an error message and nothing else happens."
The fact that compatibility mode had an effect on the problem is significant. Unfortunately I know very little about how compatibility mode actually works, but exploring this area or seeking an expert opinion might be worthwhile.
GOG uploaded a new installer recently that fixed the pagefile error, have you tried this version? (probably won't solve your issue, but it is nice for the pagefile fix anyway).
Again, I'm just shooting from the hip here, but I'll do what I can to help.

You didn't mention if you verified the MD5 checksum for the download. Maybe something is corrupted somewhere?

@ GeneralAdmission:
I still appreciate it. Shooting from the hip is better than nothing - and actually one of your tips might prove useful. Disabling automatic reboot on system failure allowed me to see a BSOD-report that suggests ctoss2k.sys is somehow involved. A quick search on google reveals that I'm not the only one having problems with that driver, so hopefully I'll be able to find some useful information on that subject.
@apeman:
Thanks for the suggestion, but I've already tried that. I intended to put it in my previous post and I don't know how it got left out - sorry about that! At any rate, the checksum was verified.
UPDATE: I nailed it! Updating the Audigy drivers did the trick. (It appears Creative released a driver update this summer. The last on was a couple of years ago, so it didn't occur to me to check.) I wouldn't have realized it was a sound driver issue if it hadn't been for your suggestion to turn of automatic reboot, GeneralAdmission. I really appreciate your help.
So now I can run the game, but I have severe performance issues. The menus are so sluggish I'm barely able to position the mouse pointer where I want to. As I understand it, this is a common issue with patch #3 and ATI drivers. The fact that the Demo runs silky smooth with every setting maxed out supports that theory. Any suggestions?

Mmm.. I normally hate suggesting the following but.. here-goes.
1) Are there any beta drivers or release-quality driver updates available?
2) Maybe rolling back to a previous version could help.
I don't have an ATI card/chipset, so I wouldn't be able to test these out myself.

No worries. As we've seen in this thread, you never know what kind of advice will turn out to be helpful.
I'm currently running the latest official drivers from ATI. There might be beta drivers available, I'll check on that later. I know they offer a wide selection of older drivers to download as well, but since I've seen reports of pacth 3's performance issues dated as far back as when the patch was released, I doubt older drivers will be of any help. I'll look into it, though I was hoping the Sacrifice community would have found a workaround since 2001.
For the time being I've been able to "unpatch" Sacrifice to version 2, so I can at least play through the campaign, and oh boy is it worth all the trouble! :)

Run sacrifice, when the black screen with the option to change your display driver pops - Open your task manager go into Processes and right click sacrifice.exe -> Set Affinity
You will see CPU 0 and 1, uncheck CPU 0 and click ok. Exit the task manager and continue to running sacrifice, see if it loads
If it doesn't then my only other suggestion is installating older drivers of your ATI video card.