|Your mboard model cannot support 3.3v / 2X AGP, but it is NOT harmed by video chipsets that DO support it.|
Your FX5200 video chipset DOES support 3.3v / 2X AGP - it supports 1X / 2X / 4X / 8X AGP .
E.g. see here:
If your FX5200 video chipset is on an actual physical card installed in a card slot, I have never come across, or heard of, an AGP card that does not all the capabilities of the card's video chipset wired up.
You probably must use a low profile card - it has a shorter standard metal bracket for attaching it to a case card slot at one end - or one that has both standard and low profile brackets included.
"....tend to indicate your power supply is probably not very powerful. The power supply will determine what replacement card you can use."
Your power supply must have at least the minimum capacity required to support a system with the graphics card you are using installed, or the max graphics card you might install in the future.
(Onboard video - video built into the mboard - IS NOT A CARD ! )
If that info is not in the ad for the video card, you can go to the video card maker's web site and look up the specs for the model - often under system requirements - the minimum PS wattage, and, more important, the minimum amperage the PS must supply at 12v is stated. If you don't find that, any card with the same video chipset including any letters after the model number has very similar minimum PS requirements. Some power supplies have two or more +12v ratings - in that case, add those ratings to determine the total +12v current capacity.
Look up the specs for your Asus Terminator barebone specific model and find the power supply capacity rating. If that's 250 watts or less, there are very few video cards with video chipsets that can be used with such a low capacity power supply without causing you grief and the power supply likely eventually failing.
E.g. one newer (first released later) than yours video chipset I found that can be safely used with a 250 watt PS, other than the FX5200 - NVidia 7200 GS - there are lots of cards with that on the web.
In some cases, if you search using the (Asus in this case) part number on the small form factor power supply to search with on the web to find replacement PSs that will fit in your small form factor case, there may be some that have a higher capacity rating.