If it's the first dive and you abort it accordingly, then you take your max depth and dive time and use the tables normally.
I am not arguing against computers, I like them. I am not arguing against a backup computer, that's a fine approach, I am just suggesting that with a good knowledge of decompression theory and some background in both table and computer use, the ways there are to skin the cat increase.
I realize that our positions are really quite similar and we are just quibbling fine points.
As I said before, if you glance at your computer 60 minutes into a dive (multi-level with a max depth of 100 feet) and see that it has stopped working at some point after you looked at it last, even if it was only a minute ago, then you have no way to get back on the tables.