I have downloaded all the files in your gallery folder (including the .DS_Store files which are not generated by JuiceboxBuilder-Pro) and have recreated your gallery's structure on my own hard drive.
I have no problem opening it in JuiceboxBuilder-Pro (v1.4.1) on my own computer so there does not seem to be a problem with the gallery itself. This was likely to be the case but at least now we can rule out gallery errors as a possible cause of the problem. The problem certainly seems to be isolated to your own system somehow.
To summarize the above (and for anyone else experiencing a similar problem), here is a comprehensive list of things to check/try:
(1) Make sure that you are logged in with a User Account which has administrative rights. If necessary, create a new Administrator User Account and install Adobe AIR and JuiceboxBuilder-Pro from within this new account. (Windows).
(2) Make sure that you are using the latest version of Adobe AIR (v14.0) which can be downloaded from here.
(3) Install Adobe AIR not just by double-clicking the 'AdobeAirInstaller.exe' installation file but by right-clicking it and selecting 'Run as administrator...'. (Windows)
(4) Uninstall any existing version of JuiceboxBuilder-Pro:
Mac: Delete the 'JuiceboxBuilder-Pro' file from the Applications folder and empty your Trash.
Windows: Use the uninstaller in the 'Control Panel -> Programs -> Uninstall a program...' list.
(5) Make sure that no files are left behind from any existing version (or failed install) by manually deleting the following folders from your hard drive:
Mac: /Users/your_username/Library/Application Support/Adobe/AIR/ELS/JuiceboxBuilder-Pro
Windows: C:\Program Files (x86)\JuiceboxBuilder-Pro
You may need to Show hidden files to find some of the above locations in Windows Explorer.
(6) Search your hard drive for the term 'JuiceboxBuilder-Pro' and delete any and all entries found (to be absolutely sure that nothing remains from a previous or failed install).
(7) Ensure that the 'JuiceboxBuilder-Pro.air' installation file is on your Desktop or in a non-restricted folder on your hard drive (and not on an external or network drive).
(8) Disconnect/unmount all drives other than the main hard drive (including time machine backups). (Mac)
(9) Ensure that any security software that you may have installed is not interfering with the installation process.
(10) Install JuiceboxBuilder-Pro following the 'Installation' instructions in the JuiceboxBuilder-Pro User Guide.
Try installing JuiceboxBuilder-Lite (from the Juicebox-Lite zip package available from this web page).
You can install and run both JuiceboxBuilder-Lite and JuiceboxBuilder-Pro side by side on the same computer.
If you can open the gallery with JuiceboxBuilder-Lite but not with JuiceboxBuilder-Pro, then this indicates that there may be something wrong with your JuiceboxBuilder-Pro installation, in which case, I would, once again, try closing JuiceboxBuidler-Pro, deleting the ELS folder (from Step #5 above) and re-opening the application.
This has been known to solve problems with the buttons on the 'Start' tab not functioning.
If you cannot open the gallery in either JuiceboxBuilder-Lite or JuiceboxBuilder-Pro, then there may be something on your system preventing the gallery folder from being opened and blocking the functionality of the 'Open Gallery...' button. Please check to see if you have any security software installed which might be interfering with the JuiceboxBuilder applications.