Sorry to say, but you should have put it in the garabage. Ground beef is handled many times at the butcher's shoppe. First, it comes in whole, then it's placed on a cutting board where it's broken down, then it goes to a grinder, where it's ground. Then, it's packaged and weighed. From live cow to your refrigerator there are at least a dozen different ways the meat could have come in contact with bacteria (slaughterhouse, truck, cutting board, grinder, handlers, etc...) in addition to what would normally multiply on the beef. As soon as your package thawed to 40 degrees that was when you had to cook it, or refrigerate it (you never should have defrosted on the counter in the first place, the ease of slipping into a danger temp. zone is great).
The meat can only safely be above 40 degrees for 2 hours. After that, it's not safe for consumption. The fact that ground beef is handled so much more than a simple steak or roast makes it that much more dangerous.
Lots of people will tell you to smell it. You cannot always rely on smell. It's more about time and temperature when it comes to proteins and other potentially hazardous foods. I hate throwing food away, but no amount of money is worth the illness you are probably facing.
Always defrost in the fridge or in the microwave (only if you are going to cook immediately).
The preceding was a free announcement from your local food safety and sanitation faery