Just listen to this!***
YES. If you take your hard drive out, you can safely dispose of your computer without any worry of personal information being taken, as ALL of your information is on the hard drive. The screen burning/keyboard stuff is crap (no offense to the poster--just trying to emphasize this).
This applies even if your name is Leon Panetta or Robert Mueller.
Edit--DON'T just drill holes in the hd! A crafty nerd could still easily get your info off of it. Just keep the thing. I don't even trust 5 pass programs.