Where and what is the tool wrench icon? You know you can print from File > Print also. And Ctr+P will also print.
You keep refering to things you know and see on your PC, but you need to explain the issue to someone who can't see what you used to see, and what you see now.
You say by the tool wrench, but that's like me saying you can find my house near the pharmacy. Not helping much without some reference as to what is the name of the pharmacy, what state it's in, etc...
Was the print icon on the toolbar up top in internet explorer, was it actually in the middle of the web-page, was it on the side of the web-page? Was it installed by some printer utility that may have been uninstalled or having issues starting? HP Smart Print maybe? http://www.hp.com/global/us/en/consumer/digital_photography/free/software/smart-web-printing.html