Hmm... the same on my WinXp SP3 machine... after installing Killap's mod I only get the compatibility mode message, and that's it...
EDIT: I don't know what I did, but now it's running... I basically just tinkered around and selected different compatibility modes listed in that drop down menu (Win98, Win 95, Win 2000, ...) and pressed apply from time to time (but not OK). When I finally closed that window (of course with the compatibility mode turned off) Fallout 2 suddenly started... ?!

Yes. Something is wrong with the GOG version. I have no problems with the mods when i install my old CD version of the game. (Sorry, IDLE english.)

I've been getting the compatibility mode message from Killap's restoration mod, and I was able to get it to work. I restarted my computer three times after installing the mod (Maybe not necessary, but that's what I did), and then right-clicked on fallout2.exe to get to properties--> compatibility. Then I selected every compatibility option (compatibility mode windows 95), ok'ed it, tried to run it. Didn't work, then unclicked every option in the compatibility tab. Then it ran!
Probably an overly detailed explanation and I have no idea why it worked, but there you go. Hope some of you have luck with it.

When I installed the fallout2 restoration mod I got the compatibility error as well. It was frustrating. Because even after I un-installed it, there was the same error message when starting it up again.
I looked around online (and here) and found that the right-click desktop icon properties Compatibility tab was set to on now... curious.
So I turned compatibility off and it worked... Then of course I found all my save game files were corrupt and invalid! Doh!!!
Didn't read the small-print showing that it wasn't safe with pre-existing save-files. So I started a new game! it's working great!

When running Vista I had the same error message.
I solved this by first turing on every compatibility option I could find.
And then turning them off.

Thanks so much i was freaking out.

This is working. Normal installation then F2 Restoration Patch 1.2, then one try without changing compatibility mode, error, then one try with compatibility mode win95, error then desactivate compatibility mode and it's work. Then apply high resolution pack and all is working fine, for the time. I need to refinish F1 to have a very highfull game off play.;..

I have these two mods installed -
http://www.nma-fallout.com/forum/dload.php?action=file&file_id=164
http://www.nma-fallout.com/forum/dload.php?action=file&file_id=715
And the game crashes randomly. I'm assuming one of the mods, or both/a conflict cause it. Obviously I reverted back to old Klamath after grabbing lots of stuff but who knows what it might've done in the mean time.
EDIT!: It stopped crashing, apparently a reboot was all that was needed. Very strange. Anyway, they seem to work just fine.

Oh man, I never would have expected it was something that simple. Now I can finally try a bug free Fallout 2, thanks a ton.

Does anyone know how to install the F2 restoration project with a GOG downloaded copy of the game?

Of all the mods to have a problem with, it had to be this one...I can't seem to get the Character Editor to work. It won't recognize the SAVE.DAT file. I'm somewhat inexperience with character editors in general, so I'm probably doing it wrong. Any advice/tips/warnings?

Thanks! now on my first play through the game will be modded to the extreme!

Is there a mod to play in windows mode?

Fallout:Beyond Good and Evil is set to be released by Christmas 2009.
http://www.towerofcreation.com/en/about
Vintage Firearms Mod Changes some weapons in Fallout 2. More info inside the link..