A video memory test should be designed to verify that the graphics chip can read and write data correctly with the memory assigned to the chip. That memory can either be built into the graphics chip, be a separate bank of memory (from main memory) or be a portion of the main memory itself. For your particular ATI video chip, it appears that it has 128MB of dedicated DDR memory (integrated into the graphics chip or attached as separate memory in a multi-die package). If the memory inside the graphics chip has developed an error, then you would have to replace the entire ATI chip. Why this happens is usually due to a manufacturing defect which has taken some time to develop into a hard failure. Other causes can be attempting to operate or overclock the system beyond its design parameters. In those cases, the "defect" may be fixed by reverting back to standard operating conditions or permanent damage may have resulted.
I would assume that something caused you to run the PC Doctor video test in the first place, yes? Something like seeing random bits/blocks/lines on the screen?