I had seen something like this before:
This application has failed to start because pscore3.dll was not found. Re-installing the application may fix the problem.
In the text of the error message, does it show the version of pscore3.dll?
It’s possible that v10 isn’t installed right. Can you make sure the PSQL\BIN directory is in the path? Can you check the actual PSCORE3.DLL.
One tool that I use is msinfo32 (Start>Run>msinfo32). Launch the utility and click Software Environments>Loaded Components. Scroll down until you find PScore. Here is an example of a default install:
Name, Version, Size, File Date, Manufacturer, Path
Pscore3, 3.10.14.0, 297.28 KB, 5/1/2008 7:08 PM, Pervasive Software Inc., c:\program files\pervasive software\psql\bin\pscore3.dll
So check the path first. You may want to uninstall then reinstall PSQL then PBA. Opening a ticket and have a support tech may be an option as well for more detailed support.