Either your card is malfunctioning, or there is a conflict somewhere in the hardware/software (the latter is usually the case, but not always). If you can give us the make and model of your computer, with as many details as possible, it will be easier to recommend a course of action.
Basically, the ATI tech was suggesting your motherboard (MB) may have a built-in graphics card (integrated video) that is conflicting with your add-on graphics card. Easy way for you to rule that out is to check the back of the computer to see if there's another VGA connector your monitor could plug into. If there isn't one, then that's not your problem. If there is, you will have to enter the BIOS screens as ddogg mentioned and check to make sure it is disabled (usually pressing f1, f2, or delete during a critical time at early boot-up is how you get in - the actual instructions often flash by on your screen very quickly during this time). The BIOS screens can look a little confusing, so it's hard to advise on where to look exactly.
The other obvious possibilites are software conflicts, hence the recommendations by members here to install the latest version of Microsoft's DirectX (available from microsoft's website or windows update) and ATI's latest driver (you should get the display driver and control panel download, but not the one with Catalyst Control Centre since it involves you also getting microsoft's NET framework, which is one more headache than you need right now). You also need to get the latest AGP chipset drivers. This is a little trickier, because you need to find out who made the chipset for your motherboard. It could be either Via, Nvidia, Intel, Sis, etc. An older version of this driver often comes on the CD with your computer/motherboard, so that should help you track it down if you have one. Otherwise, you will have to look under your windows control panel system icon for more info (we also need to know which version of windows you are running, etc.).
Hope that helps get you started!