In my case my house was burgled last year and amongst other things my wallet with many of my C-cards was taken. I've never bothered to get them replaced, so I also don't have a current C-card. On log books, I used to keep a paper one, then transferred to a computer record. That started out using the software for my then computer, but when I changed computer found no migration path for that data so it became inaccessible to me. From that point I transferred to a spreadsheet of my own devising, which I backed up twice along with all other data. Believe it or not, I had two hard disk crashes on different machines at the same time, one of which was whilst copying data from one to another. The upshot was that I lost all records at one instant. At that point I gave up, and have never bothered since. In any case, a computer record can readily be forged, albeit laboriously.
When I went on my PADI IDC back in the mid-90s, there was one candidate who had bought all his C-cards without doing courses and who had forged what he thought was a credible-looking logbook. The CD said that it was not the first time she had come across such a thing. I never look at logbooks, unless it is prior to a particular technical course and I need to see evidence of specific dives, and even then I only accept what is said for a particular dive if I recognise the signature of the instructor/buddy. If someone turns up wanting to dive but without C-card or logbook, if I believe them I let them. I can tell within a minute or two if they are bull****ting me.