Two things spring immediately to mind:
- Are the motor cables connected properly?
- Have you uploaded an actual program to the brick?
There is at least one way to connect the cables, at either end, such that the motors will not work. For this test, make sure the cable wires go out toward the "back" of the brick and the motor.
And, AFAIR, "Run" doesn't do anything with the motors unless you have uploaded a program that actually turns the motors on. I'm no longer familiar with the shipped software, so I don't recall if the process you describe actually does more than upload a firmware.
So, ensure that you are actually putting a program on the brick that turns the output(s) on, and those specific outputs are actually connected to a motor in the correct manner.
My quick test is usually to use the IR remote to tell the brick to enable A, B, or C outputs in either direction. You can also use the lamp to test; if the lamp lights then the output is on, and will also drive a motor.
Also, if you press the View button a few times, it will show a cursor next to an input or output. If the IR remote or program toggles an I/O, you will see the display change to indicate the state of that I/O.
(I see that I missed a key point: the Run button does not beep or change the display. This indeed points at a hardware problem, and not a config issue as I discuss here. If so, a quick-ish solution might be to get some of that contact cleaner stuff ["CRC QD Electronic Cleaner"], pull the batteries and squirt a little of that into the spaces around the button.)