Oh, and I am using SliTaz 3.0.

Open terminal:

lspci

Enter
Post the output to identify the VGA hardware.
Google indicates you'll most likely need the linux-agp.tazpkg and setup intel_agp kernel module to autoload as well as an intel video driver.

Start here: http://doc.slitaz.org/en:guides:xorg-xvesa / Using Xorg & Vendor-Specific Drivers / AGP Cards

It says:
00:02:0 VGA compatible controller: Intel Corporation 82830 830 CGC [Chipset Graphics Controller]
00:02.1 Display controller: Intel Corporation 82830 CGC [Chipset Graphics Controller]

I went ahead and installed SliTaz from the command line.

Okay, I followed all the instructions for Intel drivers at your link. After installing the driver, instead of showing strange colors I just get a black screen. I don't know if I clarified it before, but I never had any real picture, just a screen that changed slowly from black to white to gray. However, now I can type startx and it doesn't tell me that x is already running. Instead, after switching back to tty1 I see:
Fatal Server error:
Caught signal 11. Server aborting
pcmanfm: Fatal IO error 104 (Connection reset by peer) on X server :0:0.

and several similar errors from lxpanel and XIO.
I'm guessing something about the Intel driver is causing X to fail when it tries to start. I deleted Load "intel_agp" from xorg.conf, but it didn't change anything.

Laptop video setup with xorg on slitaz without any prior experience is pure torture.
Based on google searching xorg-xf86-video-i810 is the linux driver of choice for Intel Corporation 82830 830 CGC
For some reason slitaz dev team add i740 and drop i810 for slitaz-3.0
According to wikipedia i810 graphics is based on the i740 2D/3D accelerator
Maybe it's worth trying the i740 ?
Easiest alternative would be to dump xorg and run slitaz-xvesa flavor.
A good tutorial would be how to install tinyx-xvesa server on slitaz-3.0 xorg version.

@mojo - you cannot use tiny-xvesa with xorg - either you use slitaz-3.0 xorg with the vesa driver or the Xvesa iso. Slitaz changed in 3.0 to use xorg instead of tinyX, because tinyX is not developed any more.

@philipk88 - I have a Computer with i810 video driver around - it is still running vecor light, because I had quite lot of troubles to get X running, but I have no time now to test.

you need agp and what I remember did the trick was in xorg.conf:

Section "ServerFags"
Option "AIGLX" "off"
EndSection

but this was with the i810 driver, but perhaps it works also with the intel driver or the i740

It works! I added the ServerFlags section and changed driver under the device section from Intel to i740 and the desktop started right up! Thank you both very much!!

@ philipk88can you change the title to solved and change perhaps to "colors-go-crazy on intel i810 grafic chip" - so it is easier to find ....

Oh yeah, I almost forgot to close it. Thanks again!