Noels entry for the Open 7400 Logic competition is a 74LS00 based full wave rectifier.
I want to have an entry that it simple enough that other people can try out with their breadboards. Something that is easy to do, and yet feature a mis(use) of a typical 74LS00 IC.

Interesting.
Many TTL NAND gates are really nothing more than a bipolar NPN transistor with multiple emitters, one per gate input. My first assumption was that Noel had directly used the transistors making up the NAND, instead of just the input pin protection Zeners.
As for the 10.4 V DC operations, one should keep in mind that an Absolute Maximum Rating of 7 V is not a guarantee that the part will break above 7 V … it’s actually a guarantee that the part will not break below 7 V. In order to guarantee that all parts will work with up to 7 V, the manufacturer has to let a few of them work at 10.4 V DC. The rare few that work at 10.4 V do not do so because the chip is being used differently that what it was designed for, but rather just a lucky strong chip from the batch. I think the example of this is that Noel blew up some of the inputs during his experimentation – hardly proof that he was able to successfully defy the Absolute Maximum Ratings just by using the chip outside the designed purpose.