Here's my doltish response to your rude chastising of people trying to help you.
When you enter a contact into your phone, when it prompted you to save them, so you remember saving them to the Phone, or to your Gmail account?
So, What carrier are you on? That would be helpful to know, as someone on the same carrier may be more specific. A nice person responding to you above tried to give a example: I am on Verizon. If my contacts were saved to the Phone, then Verizon's Cloud backs these up. Verizon Cloud can be accessed from a computer after logging into your account, view the Cloud contact data, export this file to be saved elsewhere. Other carriers may have a similar setup.
If your contacts have been entered into your Gmail account, you simply have to log into Gmail from your computer and look at your contacts. Google 'how to export Gmail contacts' to a file (for safe keeping), as I don't have this process memorized.
Contacts on the phone are not stored in a normal file structure like vCard, VCF ( common file format for contacts that are exported). They are instead in a file format akin to an SQL database, not readable just by connecting your phone to the PC. And by the way, there are system settings you must have already enabled on the phone in order for your phone and files to be seen from your phone connected to your computer, such as USB debugging on, and USB mode already set to File Transfer. If not set already, with your dead screen, it could not be done easily. There are some work arounds you can Google, but they are tedious; if you are desparate.