Check your connection strings: the whole idea of SQL Server is that multiple PC can connect to it, an dI absolutely guarantee that it works!
It could be as simple as you trying to use "localhost" on both PC's, or as complex as an Authorization failure due to your login permissions. We can't tell because we have no access to your network, let alone your server and connection strings.
I don't know if this wo=ill help, but this is how I manage connections:
Instance Storage - A Simple Way to Share Configuration Data among Applications[
^] - if it works for one app, it'll work for the others without config changes.