Apple has a few different ways to identify your Mac mini. I'll link the article [link|https://support.apple.com/en-us/HT201894|here|new_window=true], but the spark notes of it are that you should be able to find the information about your machine if you click the ***Apple icon*** in the upper lefthand corner and under ***About This Mac.*** If the machine can't boot, then you're going to want to use the serial number that is printed on the bottom of your machine along with [link|https://checkcoverage.apple.com|Apple's Service and Support Tool|new_window=true].