The new version may put some files or changes in the registry which is not removed by the uninstallation. When you install version 3 the installer may detect there is a new version there so it stopped. Do you have a system restoration point created recently. You can check system restore of Windows because under some settings the system will create a restoration point for you automatically whenever you install a program. You can roll back your computer to the status before you install Photo Explosion 4 there. I mean the system restore in the Windows System Tools if I didn't make myself clear.
Also, you did not upgrade your operating system after the installation of version 4 right? You can check the Control Panel and Program and see whether there are some fundamental stuff installed with version 4 such as .net framework or C++ runtime or redistribution package or something alike. To uninstall them may fix the issue also. Please don't hesitate to let me know if you have any more questions.

Because you didn't deleted registry from your system for v4. Go to registry editor and path through until you find registry directory. After deleting only that registry, restart windows and install v3.