I think I may have found the part that's causing trouble here.
In fb/fbpict.c, there's a function fbHaveMMX that uses inline assembler, and appears to check for a 486 before trying to use CPUID. The Cyrix chips support CPUID, but it's turned off by default (!!), so trying to use it here makes the processor throw a SIGILL. (The kernel should be enabling this, but in 2.6.16 it's not fsr...)
I'm going to check my kernel config to make sure the Cyrix hacks haven't been removed or disabled; if that's the case, I'll check with that kernel and report back. In any case, this doesn't appear to be a problem with X.org as much as it is a faulty kernel config.
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