I did not attempt to run the program until after I replaced the EXE file from the zip file. After running LASetup.exe, I went to the install location(C:\Program Files\LogAnalyser), and renamed the "LogAnalyser.exe" to "LogAnalyser.exe.old". I then extracted the zip contents to that folder.
Just to make sure the original file didn't muck things up, I went ahead and ran the original EXE file so that it was the unregistered version, and then re-ran the patched registered copy and it still worked. So this isn't going to matter to the new EXE file. What I'm saying is, there isn't a file or registry entry that will prevent the new EXE from running as registered.
I looks to me like you're having a permission problem. Make sure the login account is either part of the Admin group, our just simply log in as the Administrator and replace the file. If you are an Admin, you're doing something wrong, and you will have to figure that out..