Kernel panics immediately upon powering on and shuts off

Hi! I acquired a large quantity of 12" iBook G3/500s, and while a good quantity of them work fine, many of them (about 30) kernel panic immediately upon powering on and shut off. They do sometimes boot up fine and work for as long as you keep them on, but then they tend to shut off again when they are rebooted. They usually start working again when you make a change (i.e. add RAM, reset PRAM), but just when I think I've fixed one of these machines, it starts shutting off again. My first suspicion was that it was a memory issue, however they are just as likely to do it when all expansion RAM has been removed. I've tried resetting PRAM/PMU, loading an image vs loading the OS manually, and all the usual stuff. The interesting thing here is that there are so many similar machines acting in a similar way...it makes me think the cause of the problem must have been environmental, or that they all came from the same (bad) batch? Anyway, if you have any thoughts I'd be very interested to hear.