Hi Peter
You appear to have tried all the obvious things.
It sounds like it is either an OS issue or a corrupt version of MS Office to me. What I suggest you need to do is backup all of your data to an external drive for safety.
Then reset your machine back to factory settings.
Then re-load MS Office (nothing else). Test Excel to see if you have the same issues. If you do it may be that you have a corrupt version of Office. If so you could try downloading a trial version of Office and test that. If that works you should be able to use your original Licence Number to activate the trial version.
Hope this helps.
Good luck.
Tony