Fortunately, a while ago I came across this tool: Darik's Boot and Nuke. This is basically an image file you download and burn on a CD. You boot the computer you want to recycle/give away/sell with the CD and it just wipes all your hard drives.
I used it with both computers and it worked perfectly. Now I can give them away without concern.
Oh, using this software had an unexpected bonus! Because I had to open the CD drive, it stopped me from sending the computer away with a backup CD in it!