I have had some problems previously with installing some versions of PSP but none with this version.
I will presume that you have a legal version on disk or downloaded.
One thing that can interfere is firewalls , and antivirus programs and even in one case Hardware acceleration.
Disconnect your internet, Boot up your computer and then in the system tray turn off antivirus and as many programs running there as possible. Any other open windows should also be closed so that PSP X4 installation almost has a monopoly of the computer.
See if that works - I have been able to install it on a Windows 7 Home Premium Toshiba Laptop without any problems.
If there are further problems you might do a google search.
Systems XP, Win7, Win 8.1,Win 10 14393.693