Getting Drupal to work again, locally

I've been having a lot of trouble lately, getting Drupal to play nice on my local setup. Both when I was using the old P2, and now with the laptop, whenever I tried to make use of the local Drupal setup (using a copy of the live database) the child process of Apache would crash, with nothing logged by either Apache or PHP.

On Noodle (the Pentium 2 system) I wrote it off simply that the computer couldn't handle it. But having experienced the same problem with a different version of Apache, different version of PHP, a different version of MySQL and a different operating system altogether...

I wonder if it has something to do with using mod_php as opposed to doing things the CGI way. Somehow I doubt it. But I need to figure out the problem.