I thought this was the case. I think I'll just have to "retire" the motherboard since getting another graphics card with an AGP interface would be nearly impossible. The motherboard doesn't have intergrated graphics either. So, into the bin it goes.
Thanks for your rephly.
You don't necessary need a video "card", but you do need a working video "chipset", which is what produces the video signal. Whether that chipset is made available via an add-on video card or integrated/on-board graphics doesn't matter. But you have to at least be able to generate a video signal from one or the other. Afterall, that’s what is being captured and forwarded to your remote desktop client.
So if your add-on video card is failing and you don't have on-board graphics as an option, then eventually you will need to replace the video card in order to continue using RDP.