Mac Pro 10.7.5

Try booting from another system., If you are running Etre you have reason to and anyone should have multiple bootable system or clone or create one. You may just need to do a clean install (time to buy SSD device if not already!) and build a new system and data drive.

No, the fact the program won't run doesn't tell anything. Bad download? bad disk? RAM or disk error? who knows...

What happens if in your Etrecheck results you click on the link that says "click for details"?

Try running Apple Hardware test

Using Apple Hardware Test - Apple Support

or Apple Diagnostics

https://support.apple.com/en-us/HT202731

which every is applicable to your model Mac

What happens when you do this which in in the AHT link

Using Apple Hardware Test on computers with OS X v10.7 and earlier

AHT is located on the Applications Install Disc 2 and should be included with your computer or the MacBook Air Software Reinstall Drive on a MacBook Air (Late 2010). To start AHT on these computers make sure the Applications Install Disc 2 is inserted into the built-in optical drive, external Apple Superdrive, or for the MacBook Air (Late 2010) be sure the MacBook Air Software Reinstall Drive is inserted into a USB port. Then, follow steps 1-6 outlined in the previous section of this article.