I have WindowsXP (yet)

I tried to launch any of the Heroes Chronicles chapters and they all crash on startup claiming the memory cannot be "read" or something.

I lurked for the solution and found the affinity solution, tried that, still refuses to launch.

Please help?

Did you try this -
http://www.gog.com/forum/heroes_of_might_and_magic_series/heroes_chronicles_does_it_suffer_from_the_multi_cpu_bug/post10

Yes, just as I said.

Also, I tried Chronicles on Win8 computer with 2-core CPU and it works out of the box

If under the words "out of the box" You meant the original boxed Heroes Chronicles games (with Safedisc copy protection) then all of them should work fine on Windows XP (x86) or earlier. On Windows Vista/7 these games should work fine as well, however, it is not recommended to install these games in 'Program Files' folder (installing and running the game as Administrator also recommended). Dunno about Windows 8.
GoG release should work too but No-CD cracks used in this release sometimes can lead to problems.

I meant out of the GOG. I wouldn't create a topic here if I didn't buy it here.

Well, it works on Win8 laptop, so that's not that big of a deal now, but still have no idea why it crashes on startup.

Hmm, try adding game .exe to DEP exceptions.

Wow, this solved it.

Thanks!