As I mentioned in my previous post, the screenshot indicated that the Essentials.pkg file was bad. Besides the DVD and DVD drive, it could also be that this error occurred because your HDD malfunctioned when the file was copied to the HDD, which appears you also suspected as being a problem. If you used the Disk Utility First-Aid to check the HDD, the tests it does are not very comprehensive. It won't catch all problems on a HDD. You said you tried it on another computer - does it actually boot and run or does the computer just recognize it? If you haven't tried booting and running the OS from other computer, it doesn't say that the HDD is OK.
You need to isolate each of the problem components and test an alternative to see what your problem is. So, if you suspect it's the HDD, that would mean trying a different HDD to see if it works. There is software which can do more extensive testing of the HDD, but they typically cost as much or more than a lower-capacity HDD.