It turns out it was related to nouveau driver (ie to my graphic card, which is bi-gpu). I could "make it work" for the time I installed proper nvidia driver by adding "nomodeset" at the end of the kernel line each time I started my computer. It seems the installation already has this option set, explaining all the trouble I did not encounter on Live CD.
However, it still is a problem, as it completely forbids the desktop's use. This "nomodeset" could be implanted in a semi-automatic way... just a suggestion. Either when seeing the graphic card is not supported by nouveau (means creating a database), or adding it to the grub for the next boot at the time nouveau crashes (these are two kernel.log examples) : "May 19 09:52:22 debian kernel: [ 27.561689] [drm] nouveau 0000:04:00.0: PFIFO: unknown status 0x40000000 May 19 09:52:22 debian kernel: [ 27.685372] [drm] nouveau 0000:04:00.0: PFIFO: read fault at 0x0008657000 [PAGE_SYSTEM_ONLY] from PGRAPH/GPC3/(unknown enum 0x0000000b) on channel 0x0002060000 [...] May 19 11:07:31 debian kernel: [ 44.401798] [drm] nouveau 0000:04:00.0: PFIFO: read fault at 0x000811e000 [PAGE_SYSTEM_ONLY] from PGRAPH/GPC3/(unknown enum 0x0000000b) on channel 0x0000a21000 May 19 11:07:31 debian kernel: [ 44.401810] [drm] nouveau 0000:04:00.0: PFIFO: unknown status 0x40000000" Then, maybe it would have been more relevant filing this bug report under the "nouveau" package tag. Cheers! Debian is working now :).
