From: Oslo, Norway
Too bad about the video card, are you sure it's completely toast? It's rare a piece of hardware just dies, I've had it happen but only like a couple of times last 15-20 years... but if it won't even post then yeah... Do you have a warranty for the card still?
The Open Save dialog is pretty much a standard Windows dialog and if it looks at the correct folder it should show the files, as long as the files are there. This is pretty obvious I guess, but make sure you're in the right folder - open the dropdown at the top to examine the path, make sure it's located in "Documents\TOAW4\Saves".
Also one thing to check is that the dropdown above "Open" is set to "Saved Games", there shouldn't really be any other option there anyway.
Try to enter an * in the File name field, it will then show all files in the directory, not just .SAL files.