Giants is an old favorite of mine. Because of GOG's Interplay promo, I decided to check if my retail edition would work on my current computer. It didn't, even after patching it to 1.4. Is there any way I can solve this problem, and if not, can I expect GOG's version to perform better?

What exactly is wrong with your retail cd? Does it simply not run?

I guess I should have been more clear on that. :)
It installs fine, and starts with the company logos like normal. Then I hear a split second of the menu music before the game crashes with a standard error message.

Well GOG spends time tweeking and fixing games to run on windows xp, vista and even win7 most the time though 7 is not offically supported yet. So it should run but with any computer related thing different hardware and even software causes different problems. So it Should run but its not a 100% guarantee.
If you do decide to get it and it unfortunalty doesn't work you can get help from the community via these boards or contact gog support and they are normally very good at helping people with their problems.

Try running it as admin and try using the various compatibility modes for the game. Worked for me on most of my old games....

It might help if you told us some system specs, like OS version, video card make/model, processor make/model, RAM amount, etc. Troubleshooting a problem without knowing a single thing about the system the problem occurred on is a bit difficult.
I can say that Giants has worked flawlessly for me since I got it from GOG almost a year ago now (first game I bought from them). The machine I run it on is by no means brand new, but the hardware is definitely newer than the game is (Windows XP SP3, 3.0 GHz P4, 2 GB RAM, GeForce 7600GS 256MB).

JudasIscariot: I already tried compatibility mode, and it didn't help. Not that I was surprised; I've never played the game on anything but Windows XP. I've forgotten my admin password, but I think that's a dead end anyway, as I never had to do that before. This is a hardware thing, not software.
cogadh: AMD Phenom II X2 550 BE, ATi Radeon 4770, 4 GB DDR3 (recognized as 3.25 GB due to 32-bit OS) and Windows XP SP3. I could give you more details, but they're unlikely to be significant.
I originally played the game on an AMD Athlon XP 2500+ with ATi Radeon 9700 Pro and 512 MB DDR, so I know it runs on hardware newer than itself. However, that was six years ago...

As your running XP you could try to turn the sound hardware acceleration down or off.

Got around to trying it now. Didn't work.

I have the exact same problem, tried many fixes and none of them worked. I've got the GOG.com version of it and am very curious of what would cause this problem. (My computer only has 2.5 ghz p4, G4MX series and 1.25 gig of ram) The response I got was to reinstal Direct X, but since I have had no problems with any other games I've gotten on GOG or elsewhere I decided to not do that again.

That solved it! Thanks, Namur! Of course, I've already bought it from GOG now. Oh well, it was only $3, and I now have the game copy protection free with a few extras for good measure. Some of the tunes have been playing in my head many times over the years, so the soundtrack is particularly welcome.
Man, Timmy is so awesome!

It seems my answer came a little late then. I'm sorry about that.
But i agree, you can't go wrong with a gog game with extras for such a low price.
Anyway, it looks like you're having fun and that's what really matters.
Cheers.

Quick note: I can confirm that GOG's version does in fact work out of the box (or file, I suppose).

These dlls also fixed the "crash on load" error for me but the sound is still pretty messed up.