Apple infinite load. I/O error and even a new HD
First I would try doing the NVRAM reset by restarting and holding down Command-Option-P-R until you hear the startup sound a second time. Then I would try an SMC reset. Mavericks and Mountain Lion can be pretty finicky and even strange when new hardware is installed. I've had to reset the SMC on my system with Mavericks 3 times since I started using Mavericks. In my case, it's Mavericks, not the hardware. It's buggy.

The I/O error typically is either a bad drive or cable, so you probably did have a real hardware problem at some point. I'd be inclined to recommend Scannerz (http://scsc-online.com/Scannerz.html) to test it, but you need a working system to use it, and if you can't even get yours to boot, that obviously won't help.

Does the Mac Mini even have a SATA cable to the HD, or is it a connector that sits on the logic board with the HD plugging directly into it?