It sounds as though your logo was a bitmap embedded in the EPS file. When you converted it, it simply created a bunch of short line segments to match. Either that or you had a degenerate vector EPS.
Do you have the full Corel suite? There is another program in the suite called Trace or PowerTrace. It will vectorize a bitmap. I haven't used it in many years so I can't give you more specific details. Depending on your EPS file, you might have to convert it to a bitmap before you Trace it.
If you don't have the full suite, there are some free ones available as well as some online conversion services. Google "free raster to vector converter".