HELP, I'm not a Mac User! Stuck in Recovery Mode.

Just got to redo the password after waiting for 11 days. This is my Mom's apple so I have no idea what I'm doing. Here is my problem, I have no idea about Mac's, Apple's or whatever you call these things! Here is what I can tell you, it's a little square box with a power cord that plugs into the wall and the other cord coming out the other side of this little box has what looks like what I used to call an RCA connector except way larger! That cord goes to the back of the display. The display has a power button on the rear of it at the lower left corner, and I looked at the back of the display and it has a couple of weird looking slots that both have lightning bolts engraved above the little slots. Okay, I know some of you out there if your really interested in this type of stuff is probably wetting your pants saying; "I know what it is, pick me!!!" Okay, maybe not, but if you've read this far, THANK YOU!!! I mean that! Here is my problem, after resetting everything Apple required for her username and Password, when I power up this little box, it comes up in recovery mode, and because the wireless keyboard and mouse can't turn on the bluetooth, nothing else happens. So I get that if I could use the mouse to click on something, I could click on her admin thing and enter all the necessary info to get her back into her macland, if I can actually get her out of recovery mode once I can control the mouse and keyboard.

So, first off, what do they call this silly box, my Mom doesn't know, and there aren't a whole lot of pictures on these websites showing anything about what exactly they are so I might sound a bit more intelligent when talking to a Maccie about what it may be? And how do I go about getting it to come out of recovery mode and actually be able to move either the mouse, keyboard or both which I think could be immensely helpful. Otherwise it's kind of like driving a car you can't steer! That won't end well. Thanks for any help in advance. As far as the device I'm using to post this is my Dell laptop because I have no idea what apple it is.

KurtOG.....