im runing at 2.0 ghz with 1.5 gig ram

Delete ddraw.dll (originally posted here)

I'm having the same problem. I tried renaming/deleting ddraw.dll, but that caused problems with the game running (screen would go black and not refresh, load screen was all sorts strange colors).
I'm running TeamX 1.2 with the high res patch. The odd part is that I have Fallout on my laptop which was installed from an old version of the retail CD runs just fine with the same patches, but the GOG version is like molasses -_-

The other solution which was also discussed here was to rename the falloutw.exe to another name (like fallout.exe in order to erase the compatibility settings GoG put to make the game compatible on every system.
You can also disable your vertical sync, it worked for some people.
We really need to do a big FAQ to avoid all these duplicate questions! :)

I'm running a Vista x64 here, no slowdowns except when I installed the high res patch. Then I removed ddraw.dll and the game runs at normal speeds. Oh. I also removed the compatibility settings on the exe. So try that too.

Do what everyone has mentioned and what I did was downloaded the fallout.php file. I you will have to look at an another thread to find it. All of those thing cured both the black screen issue and any speed problems

I applied the "sfall.zip" patch and that fixed the lag, but then I was having the black screen problem. I turned off the compatibility settings and it seems to be running normally now. Thanks cubicu07. It seems odd to me that having the compatibility settings turned on would cause a problem.
EDIT: So I totally lied. That didn't fix my problem. When I first tested it I was able to play for about 10 minutes with no problem, so I shut it off. Ever since, it's still doing the black screen though. One odd thing it's doing now is every time I turn off Compatibility Mode, it turns itself back on to Windows 98/ME. Any ideas?

That's why I said to rename falloutw.exe

Renaming it lets me turn off compatibility mode, but it still has the black screen problem. I think I've tried everything people have posted, and nothing seems to work -_-

Well, I suggest you upgrade to the latest TeamX patch (since you're already using the 1.2 patch), the latest is v1.3.4 which can be found at NMA. Though I really doubt it'll make any difference in terms of your problems.
Try reinstalling the game and patches, leaving the high res patch for last. Update your video card drivers and try tweaking the high res patch's settings. Or if you can bear the low resolution, try removing the high res patch altogether and see if that solves the problem.

After searching around on Google, I stumbled on a program some people made which fixes the refresh problem. The only annoying part is that you have to have it running in the background while playing Fallout. It seems to work though.

Can you give details? :/

I originally found out about here: http://www.gamespot.com/pc/rpg/fallout/show_msgs.php?topic_id=m-1-44673275&pid=197289
Third post down. I downloaded f01_screen_refresh.zip from http://www.labo-asso.com/php/outils/fallout.php
I'm not sure if it's required, but I unzipped it to my Fallout folder and everytime I play I just open that app, and let it run in the background.