I have seen suggestions for switching these two items:
ds3d=1
eax=0
If it is currently 1, change it to 0, and vice versa. Try each setting individually then try changing both. Try all 4 combinations (ds3d=0/eax=0, 0/1, 1/0, 1/1). If none make a difference for the better put them back where they were before you started.
It does look odd that
Video Mode=1024 is under [PREFERENCES]. Try relocating it directly under [Alpha Centauri]. As above, if it doesn't help, put it back.
Also, I've read several times that with
Video Mode=1024 you won't see the
(linked) tag on a Network Node in the facilities list in the base management screen (meaning an Alien Artifact is linked there). Something to keep in mind. IMHO, the game looks just as pretty at 800x600

.
The next two are not likely to be part of the problem, but I've thrown them in for reference.
Unless you really
really like it and just
have to see it every time you play

, change
DisableOpeningMovie to
1.
Eventually you will want to switch
DontResetBeginnerPrefs to
1 (This is so you don't have to go into the game preferences menu and re-do all your selections

if you have a specific set-up you use all the time).