Had the same problem a few years ago, they were sold at a yard sale, (didn't know they were still in the bag). Anyway, start a new logbook with estimated time. Next submit a PRIA request to the FED's, they will send you any history they have on you, ie; 8710's, medicals submitted by FAA flight doc's or any other bad thing's you have on file with them!
The 8710's will show what ratings you have and will also show how many flight hours you had when those ratings were obtained. This along with a new logbook will suffice for an airline, of course with some explaining, and of course the big lesson learned!! When you apply with a company and they perform a background check, they will get those 8710's and other doc's from the Fed's so you are covered! I was told by an inspector to keep those copies from the PRIA check handy, they can fill in some blanks and give approximate flight times during your aviation career!! When I applied at my current employer, I produced my new logbook along with the doc's obtained from the PRIA and they were happy!!
Hope this helps!!