The sledgehammer idea, while funny, definitely has merit. One thing you can do is tear the computer apart, take out the harddrive, and recycle the rest. If it still turns on, you can wipe the drive with a tool like CCleaner which will run over the whole disk flipping all bits to 0. This is especially important for HDDs - Fragmentation often meant you could recover bits of data from disk sectors that were set as "free for overwrite" that weren't yet overwritten.
You can do the same (overwriting everything) for SSDs as well.
Or you can smash them to bits