If nothing happens when you click the 'New Gallery...' or 'Open Gallery...' buttons on the 'Start' tab, then I would normally recommend the following, although it sounds like you have already done this:
(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) Delete the following folder manually:
Mac: /Users/your_username/Library/Application Support/Adobe/AIR/ELS/JuiceboxBuilder-Pro
Windows: C:\Users\your_username\AppData\Roaming\Adobe\AIR\ELS\JuiceboxBuilder-Pro
(3) Search your hard drive for the term 'JuiceboxBuilder-Pro' and delete any and all entries found.
(4) Reinstall JuiceboxBuilder-Pro.
Steps #2 and #3 should ensure that no files are left behind from any previous version or failed installation.
Please also check that you are using the current version of JuiceboxBuilder-Pro (v1.4.3) by going to 'Help -> About JuiceboxBuilder-Pro...' from the drop down menu at the top. If necessary, instructions for upgrading can be found here
If you continue to experience problems, then there is a fairly comprehensive list of things to check/try in this forum thread.
Hopefully one of the suggestions in the forum thread will help.