Oracle Primavera knowledgebase states that P3 3.1 is not supported by 64 bit operating systems. Question is does the XP mode of Windows 7 Professional provide the 32 bit environment that P3 3.1 needs to load and function?
Windows Virtual PC / XP Mode in Windows 7 should allow old programs that could run in Windows XP.
Another alternative would be to use VirtualBox to intall Windows XP as a guest operating system in your Windows 7 laptop. You can then install P3 3.1 in this guest OS.