Linking Excel files in Dropbox

While I've never encountered this issue, this likely has to do with where your spreadsheet is trying to read the pathname from.
What I imagine is occurring is each computer has a different working directory and so the pathnames are pointing to the right file, but the wrong directory.
For example, you may be trying to read a filename called Doc.txt. Your computer may read a directory such as:
C:/Users/Bob/Dropbox/Doc.txt
Whereas your colleague's system may be trying to read it from:
C:/Users/John/Dropbox/Doc.txt

 In other words, you will probably want to change the pathname to a relative one. Here's a webpage demonstrating how:

https://support.microsoft.com/en-ca/help/903163/how-to-create-absolute-hyperlinks-and-relative-hyperlinks-in-word-docu

Let me know if this helps!

Cam