The podcast, How To Properly Discontinue The Use of Old Computers (available here) is good on the discontinue portion of the process, particularly the importance (overlooked more often than you might think) of insuring that all the information you need from the old machine has been replicated elsewhere.
Bearing in mind that the 'cast is only three minutes long, and of necessity very general, I'd still take some issue with the security company's perspective on wiping the disk clean of data. Symantec is of course correct about not relying the operating system's delete or desktop trashcan functions to remove sensitive information.
Likewise bearing in mind that Symantec offers disk-wipe solutions among its security and utility suites -- and the podcast is admirably low-key about pushing them -- I'd still argue that the safest way to dispose of a computer is to do so after removing the hard disk after you've wiped it clean.
And, once removed, either physically destroy, melt, disintegrate or otherwise end its existence, or store it with other data-bearing disks whose hardware homes have been gotten rid of.
Belt and suspenders? Yep -- overkill, sure, but you won't be caught with your pants down.
Nice that Symantec suggests donating cast-off computers to worthy causes or, if the junk heap is where they're headed, recommends environmentally friendly, green disposal. Here are some computer recycling sources bMighty's readers recommend.