As far as I can see, EZ Invitations has been discontinued and since I can't find it, I can't test it out for myself. My guess is that you have a different (more recent) operating system on your new computer and that may be the cause of your issues. Try running the installer in compatibility mode by right-clicking it, going to Properties --> Compatibility, checking the box marked Run this program in compatibility mode for and selecting the Windows version that you used on your old PC.
Alternatively, you can use a different application like Adobe's Spark free online service.
