I think your idea of doing this with a state machine in C is a decent one. Have you tried it? How did it work? Are you planning to write it by hand or generate it from a grammar using something like yacc?
Another thought - are you sure this has to be really fast? I've done a lot of log analysis work and it's very rare to need a lot of speed. Often it's fine if the job runs overnight as long as it produces the correct answers.
Alternately, why not throw some hardware at the problem? Can you divide the log file up and run the analysis in parallel on many machines? You'll need to add a way to combine the results from each machine, but for log analysis that's often a simple step.