Hmm. I haven't explored exactly what the LILO boot loader does (I use GRUB with the 2.4 kernel), but it would seem that LILO would do a CPU test while loading. Now, if LILO is looking for a K6 (Are you using a K7?), and it finds a K7, it might not know what to do.
Your kernel should be fine, but have you tried reinstalling your boot loader? Or, even simpler yet, to set the CPU correctly in your boot loader...
the config file should be at:
I'm no expert, though..... This may not be a good solution.