With JuiceboxBuilder-Pro closed, please double-check to see if the following folder exists on your system:

C:\Users\Username\Documents\JuiceboxBuilder-Pro\.tempGallery

If there is a .tempGallery folder in this location, please delete it manually.

The .tempGallery folder is created automatically by JuiceboxBuilder for internal use only (for the live preview window and as a temporary gallery folder until the gallery is saved on the 'Publish' tab).
It should automatically be deleted by JuiceboxBuilder-Pro on closing the application but, if this fails, it had been known to render the 'New Gallery...' and 'Open Gallery...' buttons inactive.

The only way that I've been able to replicate the symptoms that you describe is to save a gallery to a Google Drive folder (so I'd recommend not saving a gallery to a location which is being synced to an online file sharing service) and the problem seems to be due to a persistent .tempGallery folder (which has not been removed as expected).
You may not be using a Google Drive folder but a persistent .tempGallery folder might still be causing a similar problem.

Hopefully my notes above will help.

Here's what I usually recommend for users having problems with JuiceboxBuilder-Pro.
It sounds like you might already have tried most of the suggestions but perhaps the additional notes regarding security software and user accounts will help.

(1) Uninstall 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.

(2) After uninstalling JuiceboxBuilder-Pro, please check that there are no files are left behind (even from a failed installation) by manually deleting the following folders from your hard drive:
Mac:
/Users/Username/Library/Application Support/Adobe/AIR/ELS/JuiceboxBuilder-Pro
/Users/Username/Library/Preferences/JuiceboxBuilder-Pro
Windows:
C:\Program Files (x86)\JuiceboxBuilder-Pro
C:\Users\Username\AppData\Roaming\Adobe\AIR\ELS\JuiceboxBuilder-Pro
C:\Users\Username\AppData\Roaming\JuiceboxBuilder-Pro
C:\Users\Username\Documents\JuiceboxBuilder-Pro
You may need to show hidden files to find some of the above locations in Windows File Explorer.

(3) Also, please follow the procedure above (Steps #1 - #2) for JuiceboxBuilder-Lite, too (if you have it installed).
JuiceboxBuilder-Lite and JuiceboxBuilder-Pro can both be installed and run side by side on the same computer but, being that you are experiencing problems, it might be wise to completely clear your system of all JuiceboxBuilder files before trying to reinstall JuiceboxBuilder-Pro.

(4) Uninstall Adobe AIR (again, via the control panel).

(5) Reinstall Adobe AIR (as an administrator).
You can download the current version of Adobe AIR from here.
When reinstalling Adobe AIR, instead of just double-clicking the 'AdobeAIRInstaller.exe' installation file, right-click the file and select 'Run as administrator'.

(6) Reinstall JuiceboxBuilder-Pro following the instructions here.

(I realise that you are using a Windows PC but I've included notes for Mac above, too, in case any Mac users are experiencing similar issues and are reading this forum thread.)

Hopefully this will help.
If not, then here are a couple of other things to try that might help.

(1) Try temporarily turning off any security software that you might have installed (or make an exception within the software for the JuiceboxBulder-Pro executable file) in case this is somehow interfering with the functionality of JuiceboxBuilder-Pro.

(2) Try creating a new User Account (make sure it is an Administrator Account), log into this new account and try installing and running JuiceboxBuilder-Pro from there.

I hope that the suggestions above help.
Please let me know how you get on.

I'm glad you've been able to find the source of your problem.
Please let me know what antivirus program you use (and what database version you currently have installed) so that I can let the antivirus developers know about this (and hopefully they will be able to fix the problem in a future release).

Thank you for the additional information.

One other user has previously reported a problem with Avast's Ransomeware Shield (in this forum thread) back in November 2017.
At the time, I contacted Avast and they assured me that they had cleared the JuiceboxBuilder-Lite executable file's reputation in their database.
I guess the problem is still present.

I've filed another false positive report with them (via their online form).
I'll post back here when I hear back from them.