Do you see a faint image of the desktop ? The 500MHz model was not much affected by the desoldered graphic chip failure but the possibility cannot be excluded. In fact it was one of the best model of the iBook G3 line. As you say, the big problem with this one is the reed switch cable cutting in the hinge but it's a cheap repair when you can do the job yourself.
I would try all the usual troubleshooting stuff: pram reset, PMU reset, booting from an external source, etc.