Please bear with me while I try to see if I understand the setup.
Your Windows 7 computer has Pervasive data files, but does not have Pervasive installed, right?
You have 3 other computers with Pervasive installed (I assume Workgroup Engine) and they all access the data files on the Windows 7 computer. Are they accessing them through a mapped drive?
Did the previous XP machine have Pervasive installed?
If your machines have Workgroup Engine, can you tell me if they are installed as an Application or Service? The best way to check is to look in Services. If there is a Pervasive Workgroup Service, then it's installed as a service. If not, there should be a small icon near the clock that looks like a blue cylinder.
If you could also check the folder where the data files reside. When people are accessing the data, if it's through workgroup, there should be a file called ~pvsw~.loc. If you open the file in Notepad, you will see the name of the computer who is acting as the Database Engine.