A fairly dumb question about a video card.?
I am not saying this would fix my dilemma, but I was wondering if the end result could blow up my video card.
I recently purchased a used Matrox Parhelia 128m card. http://www.ixbt.com/video2/images/over2k4/parhelia.jpg . Now, at the bottom left, there is a place where a coil use to be. In the picture you can see one there, but mine does not have it.
Would it be a fair assumption that If created a mock coil with a ferrite core to replace it, that I could get it running?
I could pop one off to see what is under the hood, but I know that the core is ferrite.

No its not! It would be a fair assumption that these boards are made by the thousands and have very different components on them depending on the model. It also could be a total waste of money but even more so, it could cause a catastrophy on the card rendering it useless!
From my experience modern computer hardware is very sensitive equipment. I’m guessing you will end up destroying your video card by trying to do that. However, if there was at one time a coil on there and it got broken off then you are already screwed so go ahead. I’d just be careful with the assumption that there was at one time a coil there. I know that a lot of the hardware I have does not compare to photos I have seen on-line and that does not mean that anything is missing or broken. Sometimes they find ways to integrate parts or move them around between hardware revisions.
Your pic shows L1, L2, L3 and L10. I assume your missing L10. Unless you can get the exact same type wire with the exact same wraps and exact same physical dimensions, you are not going to create the inductance the circuit is built around. (independent of the ferrite -or not core) The device ID is clearly on there so if you rummage some used-trash electronics place for a circuit with the device you might get lucky. Your way better off trying to see if it works without the inductor (it won’t) than trying to jury-rig an inductor that would most likely create more damage than the "missing" one.