I would have left that Best Buy immediately. That sounds like total BS. My experience with Best Buy and the level of skill of their employees has not been good.
This makes no sense to me:
"It seems this is common in windows 10. I was given a choice of paying $160 to back up his old files and buy an external hard drive or pay $399 for a one year protection, virus removal etc."
I am a tier 2 computer tech for a managed service provider (MSP). What that means is small businesses like doctors offices, construction companies and the like, contract us out as their IT department instead of hiring dedicated IT people internally. So I have more than a passing familiarity with Windows 10. Yes, it makes my life miserable on a daily basis. I do not know of any common Win 10 problem that has the resolution your were given. If the geek had the ability to back up the files then they more than likely had the ability to just repair the Win 10 install on the existing hard drive without selling you stuff you don't need. I sure as hell would not have paid them $399 for a year of protection.
It infuriates me when I hear these stories. It sounds like someone was trying to take advantage of you in your moment of desperation and sell you a protection plan that I bet he/she would have gotten a commission or bonus for selling. That really makes me angry with the Geek Squad. Unfortunately, it doesn't surprise me in the least.
You should back up the files yourself and believe me when I tell you Google is your friend. If you are getting specific error messages and error codes I'm willing to bet if you search google for those you will find steps to correct the issue. As the old saying goes "There is nothing new under the sun." Someone else has likely already been there and fixed that.
Good luck!