I don't have that problem. The PAF software itself does not need to be in the Dropbox folder. I find it works best if it is not. (Each computer has the PAF software installed, as normal.)
On each of my three computers the location of my Dropbox folder is slightly different but the contents are identical. Beside my PAF databases, the Dropbox folder has my PAF media folder holding the images that the databases are linked to, so that the images appear when I open the PAF data file.
On each computer for the first time after installing Dropbox, I start PAF normally (Start button or Shortcut), then I browse to the location of my local Dropbox folder and open the file. Or I browse to the PAF data file in Dropbox and double-click its icon. (Either way will do it.)
On subsequent uses of PAF on that computer, clicking the PAF shortcut automatically opens the most recently used file (which happens to be in the Dropbox folder of that computer). When I am finished using PAF on that computer, I close PAF and allow a minute or two for automatically synching to Dropbox's web server before shutting down the computer. (This avoids creating conflicted copies of the data file.)
If your image links are not relative links, you will need to relink them one time. When your local Dropbox folder synchs with the Dropbox server (shown by the green checkmark on the file's icon), the server will then bring the other computer(s) into synch the next time they comnnect to the internet. If all of your linked media files are in the same folder, relinking may be a simple 2 minute process. If they are scattered around multiple folders it may take hours.