Well, you have to find where it's grounded, and make sure it's not grounded to something like the dash frame. Many cars have dash frames that are mixed metal and plastic, so the metal sometimes doens't connect to the chassis like you think it would/should. Also, make sure the power wire is large enough, because there is a chance that you're choking the radio from too small of a wire. If you had it installed somewhere, I would take it back to them and get them to fix it, it's not your fault at all. If you did it yourself, check all the connections to the power and ground, and that nothing is loose. It's a good idea to solder as many of the connections as you can, especially if you've spliced the head unit's stock harness to an adapter harness. A lot of people use crimp caps (ghetto) or just twist the wires together and tape over them (don't get me started).. DOn't try to get rid of the stock connector though, most cars have a quality stock radio connector and it's not smart to cut it off.

Oh yeah, make sure that you actually have the ground hooked up at all. If the ground goes to nothing (doesn't actually connect to the chassis of the car) or is missing, the head unit will usually use the shield of the antenna cable for it's ground, and that doesn't work very well. You can tell if this is happening by unplugging the antenna from the head unit while it's turned on. If the radio shuts off, you have a major ground problem.

The real answer to your question is to have someone check out a few things with a multimeter, like what the voltage is doing with the volume up, and if there is any difference in voltage between the radio's ground and chassis ground. This often isn't an easy problem to see clearly..