Can I back up after startup file corrupt?

I know nothing about this Macbook Pro but was talked into getting it. I never backed it up. I didnt even know there was such a thing. Recently there was a spinning multicolor wheel. It wouldnt stop spinning. I tried everything to get it to stop and it didnt so I restarted the computer. After I restarted it the screen was grey and there was a picture of a file with a question mark. I called Apple and spoke to the tech. They said the main start up disk is corrupt or missing. They said that I should still have all of my files but I would need to purchase an external hard drive and save everything before reinstalling the main file. I finally purchased a 4 tb external back up. How do I save my files now? It doesnt show anything once I plug it in. I cannot access safe mode either. Does anyone have any experience with this sort of issue? I would appreciate any help please. Thank you