Updating OS to support iTunes and iPhone 11

Repair HD and Permissions - Lion through Yosemite

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. When the Utility Menu appears select Disk Utility and click on the Continue button.
3. After Disk Utility loads select the indented (usually, Macintosh HD) entry from the the side list.
4. Click on the First Aid button in the toolbar, then click on the Repair Disk button.
5. If Disk Utility reports any errors that have been fixed, then re-run Repair Disk until no errors are reported.
6. If no errors are reported click on the Repair Permissions button.
7. Wait for the process to finish, then quit Disk Utility and return to the Utility Menu.
8. Select Restart from the Apple menu.

Now, try running the Catalina installer.

Are there any error messages? After clicking on the Install arrow how long did you wait for any progress? If more than ten minutes, then I'm guessing there is a hardware problem. I'd say the drive is the problem. One possibility is that the drive is not formatted correctly. It may be that it is not using the GUID partition scheme; it may not be using Mac OS Extended formatting; it may not be Journaled. These can be checked using Disk Utility. If you are using an SSD, then it must be formatted using APFS. That would require erasing the drive.

If you have an external drive that you can use, then backup your internal drive. Erase the external drive and reformat it. Use APFS only if it's an SSD. Use the GUID partition scheme. Then try installing Catalina. If that works OK, then you can restore your files from the backup.

Another thing that crosses my mind is, if you have 32-bit software running on the computer. If so, then you want to remove it. Use Go64 to find and remove any 32-bit software. Then try installing Catalina again.