You could try an absolute path to an image (i.e. http://www.etc...) rather than a relative one.
Also, the the "a href" code is adding nothing there, so I would strip it out to keep things simple.
There are a number of extensions which display images, but don't do a reload. You could try downloading one of those and comparing the code - a hybrid of the two extensions should give you what you need.
@Xavier: Unfortunately, I cannot use a text/image box here.
I am trying to get a "refresh" icon on the sheet that when clicked with reload data on that particular sheet. I got the refresh functionality working when I use a text, like say "Refresh". When I click on the text it is reloading sheet data. I only want to replace this text with an image.