I would put first a ps/2 mouse.
Is it a start from the CD or from the USB?
Do you have Xorg loaded at boot? probably not if you are starting. Xvesa?
Perhaps you can post the messages files from slitaz etc. (part keyboard/mouse) here?
Personally, I would have a look at the dmesg, Xorg.0.log.
so, in a terminal write the command dmesg > dmesg.txt (then return)
With a texteditor, open the file dmesg.txt.
Or look at the file /var/log/Xorg.0.log (or other Xvesa log files).
So, I would try following (for having a look at the log files of your PC with TCL).
Install TCL on an USB stick from another PC, with backup of .xsession you will modify, see below.
See wiki for installing the persistence (=backup).
Put in one of the startscript of TC (http://wiki.tinycorelinux.net/wiki:the_boot_process
; I would try to add at the end of the file /home/tc/.xsession):
dmesg > dmesg.txt
sudo cp dmesg.txt /mnt/sda1/_the_place_where_you_want_your_dmesgfile.txt
sudo cp /mnt/sda1/var/log/Xorg.0.log /mnt/sda1/_the_place_where_you_want_your_logfile.log
Start/boot your PC with the USB stick on it.
After it booted, takes the USB stick out and put it on another PC and look into your log files (with "fluff" or "leafpad").
Perhaps somebody has a better idea how to look at the log files.
And: Im sure we will get that thing running.
It will perhaps take few weeks.. so: patience. patience. patience.