How to upgrade from Sierra to Mojave

First, repair your disk drive with Disk Utility:

Repair the Drive for El Capitan or Later

1. Restart the computer and after the chime hold down the Command and R keys until the Utility Menu appears.
2. Select Disk Utility and press the Continue button.
3. Then select the indented (usually, Macintosh HD) volume entry from the side list.
4. Click on the First Aid tab in the toolbar and wait for the Done button to activate. Click on it, then quit Disk Utility.
5. Select Restart from the Apple menu.

Download and install upgrade: Get MacOS Mojave now from the Mac App Store.

I suggest you use the program created by Etresoft, a frequent contributor. It will provide a snapshot of your system which we can analyze to possibly determine the cause of your problem. Please use copy and paste as screen shots can be hard to read. On the screen with Options, please open Options and check the bottom 2 boxes before running. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown.

https://itunes.apple.com/us/app/etrecheck/id1423715984?mt=12

After the install hangs, have you tried shutting down the computer using the power button, and then restarting? Some times this will get the installer going again.