Q: Mac mini freezes

If this started happening without your having made any changes and without a warning of low disk space, then it's likely that the boot drive, or some other hardware component, is failing. Back up all data immediately, then run the Apple Hardware Test or Apple Diagnostics.

Even if the test is negative, you should make a "Genius" appointment at an Apple Store to have the machine tested more thoroughly.

Similar situation here. Bought mine second-hand and it is an older model. Fortunately, nearly everything I do is done on external hard drives that are attached.

And since I didn't have the admin passwords and original disks, I am attempting a reboot from my Snow Leopard disks I own. But now I'm stuck on this (see screenshot below). Anyone seen anything like this before and/or know what to do next?

Thanks.

(sorry, it's sideways)

That screen is telling yo that yo do not have a pointing device connected and implies that you had a Magic Mouse previously connected and the images is showing you to slide the power slider to the ON position.