Kern Protection Failure


I have a G5 and am having trouble accessing some secure sites. I receive a Exc-bad-access (0x001) errror. Kern Protection failure. I recently was making an imovie and after 10 minutes the movie shut down giving me the same error. (Losing all the work) I have recently switched over from a PC about 4 months ago. Additionally, I bought my daughter an Ibook and it is having some of the same problems. I did and archive and save which Applecare suggested but it didn't help. A test user experienced the same problems. Any ideas why I am getting this error?