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I just installed Debian 9 on a Lenovo S130-14IGM but the touchpad doesn't work at all.

With Ubuntu there is no problem with it.

I tried everything I found on the Internet. I have no more ideas.

Here are the results from the two operating systems:

Ubuntu

# egrep -i 'syna|alps|etps|elan' /proc/bus/input/devices
N: Name="SYNA3388:00 06CB:8459 Touchpad"
P: Phys=i2c-SYNA3388:00
S: Sysfs=/devices/pci0000:00/0000:00:17.0/i2c_designware.0/i2c-4/i2c-SYNA3388:00/0018:06CB:8459.0001/input/input17

# apt list xserver-xorg-input-synaptics
Listing...
xserver-xorg-input-synaptics/bionic 1.9.0-1ubuntu1 amd64

# dpkg -l | grep -i syna
ii xserver-xorg-input-synaptics-hwe-18.04 1.9.1-1ubuntu1~18.04.1 amd64 Synaptics TouchPad driver for X.Org server

# xinput
⎡ Virtual core pointer id=2 [master pointer (3)]
⎜ ↳ Virtual core XTEST pointer id=4 [slave pointer (2)]
⎜ ↳ SYNA3388:00 06CB:8459 Touchpad id=9 [slave pointer (2)]
⎣ Virtual core keyboard id=3 [master keyboard (2)]
 ↳ Virtual core XTEST keyboard id=5 [slave keyboard (3)]
 ↳ Video Bus id=6 [slave keyboard (3)]
 ↳ Power Button id=7 [slave keyboard (3)]
 ↳ EasyCamera: EasyCamera id=8 [slave keyboard (3)]
 ↳ Ideapad extra buttons id=10 [slave keyboard (3)]
 ↳ AT Translated Set 2 keyboard id=11 [slave keyboard (3)]

Debian

# egrep -i 'syna|alps|etps|elan' /proc/bus/input/devices
-

# apt list xserver-xorg-input-synaptics
En train de lister…
xserver-xorg-input-synaptics/stable 1.9.0-1+b1 amd64


# dpkg -l | grep -i syna
ii synaptic 0.84.2 amd64 Graphical package manager

# xinput
⎡ Virtual core pointer id=2 [master pointer (3)]
⎜ ↳ Virtual core XTEST pointer id=4 [slave pointer (2)]
⎣ Virtual core keyboard id=3 [master keyboard (2)]
 ↳ Virtual core XTEST keyboard id=5 [slave keyboard (3)]
 ↳ Power Button id=6 [slave keyboard (3)]
 ↳ EasyCamera id=9 [slave keyboard (3)]
 ↳ Ideapad extra buttons id=10 [slave keyboard (3)]
 ↳ AT Translated Set 2 keyboard id=11 [slave keyboard (3)]

What should I do?

From the Debian wiki article:

Debian 9 "Stretch"

In most cases, make sure you have xserver-xorg-input-libinput xserver-xorg-input-evdev xserver-xorg-input-mouse installed, and not the xserver-xorg-input-synaptics package.

Read: https://en.wikipedia.org/wiki/Evdev for more info on evdev.

Try apt removeing xserver-xorg-input-synaptics and installing the above packages.

# egrep -i 'syna|alps|etps|elan' /proc/bus/input/devices
N: Name="SYNA3388:00 06CB:8459 Touchpad"
P: Phys=i2c-SYNA3388:00
S: Sysfs=/devices/pci0000:00/0000:00:17.0/i2c_designware.0/i2c-4/i2c-SYNA3388:00/0018:06CB:8459.0001/input/input17

Your touchpad is not connected to the system via internal PS/2 or USB wiring, but using the I2C bus. This is a fairly new development, and Debian 9's standard kernel might be too old to support such touchpads very well. You might try with a backport kernel.

See here for instructions in enabling the Debian Backports repository - basically, add this line to the /etc/apt/sources.list file:

deb http://deb.debian.org/debian stretch-backports main

Then you should be able to install a backport kernel with:

apt-get -t stretch-backports install linux-image-4.19.0-0.bpo.2-amd64 linux-image-amd64

After a reboot, you might then have better luck with your touchpad.