Do you have the service tag of the unit? It would be much easier to find that way.
Looks like there are 3 models for the Studio 1558, and all of them use the part # 4DKNR for the motherboard as a valid compatible part.
No, sorry. I just have the following information:
Dell Studio 1558
I suspect its one of the models which include an i5 and ATI dedicated graphics combo. I think (but not sure) even some of those have varying motherboard models.