OK, thanks.
Sounds like a Mac mini (Mid 2010) from your description. To verify, does it have a SuperDrive slot on the front?
That model supports Mac OS X 10.6.3/4 Snow Leopard through macOS 10.13.6 High Sierra.
Next thing to try would be to hold the Shift key down when starting up, until you see the Apple logo. It may take several minutes for it to completely start up, and you will see Safe Boot in red letters in the upper right corner when the Desktop appears.
Let us know if that allows it to fully start up.
C