I installed Debian 10 Buster on the Asus Eee PC 1201K, with only 1 Gb of RAM and 150 Gb of disk. Notice that the CPU requires an i386 architecture. The installation is quite slow, but it completes without problems.

I encountered a problem at the first boot after installation: the boot process failed with several ACPI errors and a nasty PCI: Fatal: No config space access function found. The boot finished into the initramfs prompt where I can check that no kernel modules were loaded and no devices were available, mainly the hard disk was missing. Loading all the kernel modules via modprobe do not solve anything, the kernel does not detect the hard disk.

I finally solved the problem by installing the linux-image-4.19.0-0.bpo.6-686 and removing the pae version: linux-image-4.19.0-8-686-pae.

Installing a new package on a non-booting installation is not trivial, here it is a step-by-step guide:

• Start the installation program (I used a netinst USB stick).
• Proceed with the installation untill network is configured.
• Interrupt the installation and choose Execute a shell from the menu.

Now you can mount the Debian installed into the hard disk and do a chroot in it:

mount -t ext4 /dev/sda1 /mnt
mount -o bind /dev /mnt/dev
mount -o bind /dev/pts /mnt/dev/pts
mount -o bind /proc /mnt/proc
mount -o bind /sys /mnt/sys
chroot /mnt /bin/bash

Inside the chroot environment, you can download and install the new kernel package and do whatever you need.