You could upload the image  into a picture library. You could then reference the image from the picture library in the Image Web Part. You could also create a hyperlink  to the image from the picture library.

I've already referenced the image  from the picture library in the Image Web Part. What I want from there is the ability to hyperlink  that image to another page, so when the image in the Image Web Part is clicked the user is taken to another page.

As an example:

<a href=”some_URL” target=”_blank”><img src=”image_path”/></a>

Just use a content editor web  part and write the html code around the image.