If you suspect your Mac might have a hardware failure, you can use the bundled Apple Hardware Test that came with your Mac. These tests are model specific, so using the discs of your PowerBook on your Mac Pro will not work. If you get odd graphical errors, shutdowns, applications crash with or without a pattern, or there is some other behavior that makes you suspect the hardware, testing it is very easy. On an Intel based Mac, insert Mac OS X Install disc 1 that came with your Mac to your Mac, and hold letter D at boot. This will load it to the hardware test. After language selection, use ctrl-L keyboard combination to get it to loop mode, and select extended test, and let it run at least for a few hours. You can end the test with the same keyboard combo, or it will stop if it finds an error. For testing graphical or RAM errors, it is best to run the test at least for the evening, or even better to let it run the test overnight. If you will receive an error message on the screen, this will indicate where the error lies. (In doubt, post the error here and someone will find out for you). For PPC based Macs, use the Install Disc 1 that came with your Mac, hold down alt or option key depending on your keyboard, select the Hardware Test from the menu, and the menu selections and loop mode are as for Intel based Macs. If you don't have those install discs available, and suspect faulty RAM you could run Memtest. Memtest is an option also when you have the discs if you need to test your RAM. There is a Windows version out there, and a Mac version http://www.memtestosx.org.