The power supply is grounded through the power cable to the wall outlet. If you have it unplugged from the wall it should be a three prong plug (male) on one end and a three hole receptacle (female) on the other. The prong that is in the middle is the ground. Inside the power supply, there is a wire that is electrically bonded to the metal. Since the metal of the power supply is (typically) physically bonded to the metal of the case with metal screws, you should (in theory) have good electrical connectivity through the whole chassis. You can pick up an inexpensive outlet tester at your local home improvement mega-super-store or Radio Shack. THis simple widget plugs into the wall and through a series of indicator lamps, lets you know if your outlet is working.
Is your computer plugged into a power strip? If so, plug the computer directly into the wall and see if you get the same result. I have seen problems where a power strip was plugged into a batter back-up (UPS) and there would be interference between the two devices that caused problems with the computer (but only when the printer was on!) It's a trial and error process, but you may discover something very simple.
You could always pick up another modem as well... Just a thought...