Installing any small distro on a USB or CD will solve the problem, providing it is of comparable age to your current system.
Once you boot in the rescue distribution, mount --bind all the volatile and living data like /dev /proc and /sys (perhaps even some subdirs
from var, although i got away without this) to corresponding directories of the non-functioning system, then chroot /mnt/kernelessdistropath
and install the kernel, or any other fundamental building block of a Unix system which made it inaccessible.
Man, I used to really like Debian a lot. Four boxes in my home running it. An intern had recommended it once to me back in the early 2000s. I have an NFS server running on the i386 architecture, lots of disks, all was fine. In the living room, I had a passively-cooled "hush" workstation, also running Debian, lenny at the time. xine, vdr, streaming vdr content to the living room, mplayer, it was our web kiosk using Firefox and Thunderbird as our e-mail client. The CLE266 on board was good enough to decode DVDs and DVB-T broadcasts.
I read a lot of good things about Debian, especially the idea that the folks behind Debian prefer to be safe than sure, in other words, do more testing before they release a new version, and do not care so much about using the latest software, sounded very good to me.