Apart from finding your old logbook, you have a couple of options.
Your last medical will have the total hours as of that date on it, plus hours flown last 90 days. See if your DAME can provide a copy.
Have you emailed a CV with a breakdown of hours on it?
Start a new logbook with a Stat Dec in the front stating why there is no previous logbook.
Don't use it as an excuse to add a few 100 hours, Murphy's law will catch you out.
If you don't want to keep an electronic logbook, keep an electronic monthly/annual summary.