I don't buy paperback books anymore, so if all of the books in your series are up for free then I'd download them and you wouldn't make a sale. If there's a donation link and I enjoyed the books I might make a donation but there's no guarantee.
Putting up the first few books in a series for free when you're about to bring out the next in the series is a great idea though. I'll download and read the first one or two and if I like them will buy the next (so long as it's available as an eBook at a price I consider reasonable).
IMO (based on no evidence at all, just opinion) if you have several series, then putting up the entire of an older one may work. It gives readers a complete look at what you can do and hopefully cross sells your newer series. If you only have one series though, I wouldn't put them all up for free. One thing I'm certain of, I wouldn't have downloaded your books and have them in my to read list if they were not free. So once I've read them and assuming I enjoy them, you'll have one more customer for your next book than if you hadn't made any free
If you have a new series with a new release coming up, put up the first one or two of your new series but not the new release. Whilst I have no evidence for that working, the Baen free library stands as a good example that it can and does work.
All that said, there may be a number of other reasons why a paperback failed to meet sales expectations. It may have sold similar numbers whether you had the free eBook or not.