Missing Engine Log Book

I'm going to disagree with Denny and say it's not nearly that bad. The
engine is certified if it has the appropriate data plate (seemingly
without regard to what is attached to the data plate G). However, if
indeed there are NO logs, then at this precise moment the engine (and
hence the aircraft) are not airworthy.

Basically all you are going to need to make it airworthy is a sheet of
paper from the AI that did the last annual, with the annual engine
signoff. That done, and without evidence of anything to the contrary,
you are legal to fly. [And don't say that because there is no log book
that you don't know if anything was done since annual to make it
unairworthy. Those are independent events, and the logbook is only one
slight way you might discover such a change.]

Now... the money items: Without proper logbook documentation, it is
harder to sell the plane. Not a big problem if you plan to keep the
plane a long time (by which time you will have probably gone through an
overhaul anyway), but still an issue.

Second, you have no record of exactly what is installed in the engine.
The last annual AI will be attesting to all the AD's performed as of
that time, but you have no formal record that they were properly
carried out. Future AI *could* (and very likely might) insist that
some work be done to verify the AD's before signing off on the next
annual. And you might find yourself doing extensive work (splitting
the case) just to find that your engine didn't even fall under some AD
in the future.

Can you make a NEW logbook? Sure, done all the time. You start by
trying to get copies of the last overhaul records, plus whatever the
manufacturer might still have on that specific serial number. Ditto
the accessories. Then take all the receipts, invoices, etc. And you
make up what you can. Perfectly legal... but doesn't really solve all
the problems above.

Me? I would start with the negotiating position that the engine is due
for overhaul and reduce the price as if the engine was at TBO.