Well, maybe not good as new. At a mimimum you do need to repair permissions. I don't want to you run any "sudo" commands but you should be able to. The fact that you can't means something is screwed up.
Perhaps you should wait on deleting that Time Machine drive. It is corrupt and will certainly never work properly again, nor should you even attemp to use it. Go into System Preferences and turn off Time Machine.
Depending on what is wrong with your system you may need to restore manually.
Unfortunately, this is the only truly safe course of action for you at this point:
1) Run Disk Utility and Repair Permissions
2) Buy a new hard drive at least as big as your start up drive
3) Run Disk Utility and use its backup facility to backup your start up drive to your new hard drive
4) Now erase your old Time Machine backup
5) Create a new Time Machine backup
If your system functions normally at this point, you should be good to go. The fact that files like "boot.efi" have been mentioned make we very worried about the integrity of your start up volume. Your Time Machine is corrupt, but it may be all you have. You need another backup before proceeding. You may very well need to reinstall your OS and you will need another, valid backup before doing that.