Most EULAs allow 2 installs *at a time*, meaning that if you uninstall the software from one machine you can install it on another and be in compliance with your software license.

So, copy your back-up file (logbook entries) and install the software on another machine. After the install copy your data file to the new machine. I'd venture to say that if doesn't work on a different machine, then it's a software (Log Book Pro) problem.