"He who marches out of step hears another drum." ~ Ken Kesey
what is sounds like is that you have overprint fill may have been checked. easiest way to find out is right click on the object and your fly window which opens should have listed toward the lower portion of the fly window.
Do you still have the ability to see a print preview for a selected color? What does it display?
My first guess is that some of the blacks are not the same spot color black. For example, using clip art from different sources and combining into one file, One artist may use a spot color black and another may use a process black...and often by mistake, another artist may use a registration black as a color fill. It's also possible, that one artist used multiple blacks (including registration black).The fact that you are getting only (some) of the black areas getting added to the colors, tells me that it's more likely a registration black that is getting used as a standard black. You may already have this registration black being applied to a registration mark and might be why it went unnoticed if getting rid of all other unused colors. THIS is what the registration black is for. To be automatically added to all screens/colors even though it's not physically added to the other colors. It's used for registration marks (one time) on one layer for example, and then it gets added to all separations. It's also used on file/job info such as date, customer name, motif etc.Select the black object that is getting transferred over to the other colors, and reassign it a spot color that is far different than other colors in the art. Like Neon Green for example. Then, select all of the black elements that are not getting reassigned and color those with the Neon green spot color. This will help you see if you have any other blacks.There is a way in Corel to do this more efficiently, (basically a select same fill color) like we do in Illustrator, but in Corel I remember it's a bit more cumbersome. More steps, but I don't keep that info readily available.