sorry, its me again, I forgot some details:
Motherboard? not sure I found it can it be ASUS
Graphic: Nvidia GeForce 2 400
Processor Pentium III 1 Ghz, 128 Ram
XP Home edition
Don´t know anything else but the computer is from 2002.

Need you to clarify a couple of things:

1. What error message are you getting?
2. Are you trying to do a full install (all 4 disks) or the smaller install (first disk only)?

I tried both complete and "small" installation. In both I would go through the install preparation, the licence blablabla, etc with ok, ok, ok... as always (also have tried to install to different folders to see if that works), than the installation starts, you will follow the process with the blue bar - soandso many % installed ...) and at about 45% (small installation) or 27% (complete) it just stays there for half an hour and then the message appears and thats it.

I have the Spanish version so the message is in Spanish, it translates more or less to this:
the installation programm will end (shut down), possibly some files may remain in your system. To install Myst Exile later, please insert disc again and follow instructions.

The CD is clean, brandnew, and my drive reads everything else, so it can´t be that, or can it?

Actually I have seen brand new drives have problems reading certain disks, mostly because of copy protection.
This will sound odd, but, are you running antivirus software? If so, disable it temporarily. I have gotten blue screens of death from installers because of Norton AV.

BTW, sorry about my poor choice of words; I couldn't remember if the option was "typical" or "minimal" or what so I just used the first thing that came to mind.

If the above advice does not work try

-running the installer in Windows 98 compatibility mode.
-installing the game from a different CD-ROM drive if you have one.
-check in the event viewer to see if there are any details about the error.