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MacBook pro running 10.7 or later have Recovery (a minimal special-purpose Utilities-only system) on the boot drive, separate from the main MacOS partition (the one that will now not start properly). Recovery can also download and re-install MacOS from the Internet.

Hold down Command-R at Startup to activate.

Macbook Pro after about 2011 have Internet Recovery in their ROM, and can download Disk Utility and the other Utilities. They can also download and re-install MacOS from the Internet.

Hold down Command-Option-R at Startup to activate. You will see the spinning globe for a while, as it downloads stuff.

This article has just been re-written to include all the newest features in MacOS 10.12 and later. It is reasonably accurate, but some features work slightly differently in older versions:

About macOS Recovery - Apple Support

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That "prohibitory sign" tells you crucial parts of MacOS are damaged, and starting up in the usual way will be impossible.

If you DO have a Trusted Backup, and are confident that your drive is working properly, you can do a re-install-in-place. This re-writes over 350,000 files, but does not bulk-erase anything outside of System Directories. By design, your files and your added Applications are not touched.

if you do not trust your drive, or do NOT have a Trusted Backup, that drive has your only copy of important files. Do not change it. Instead, obtain a drive that could be used as a replacement for your current drive, and an external enclosure or adapter to hold it while you Install MacOS from scratch. When you are confident it is working properly, you can attempt to rescue your files, using the full capabilities of MacOS and possibly other utilities if needed.

About the screens you see when your Mac starts up

How would you do a re-install of Mac OS if you have the grey screen as it is impossible to use any of the keys?