I recently purchased a new home and in the Living Room the floors were replaced w/ a dark unfinished Veneer. I have a dog and the slobber is leaving white marks on the floor. I am having a hard time finding anything that will clean this floor without leaving spots. Someone suggested straight Murphs oil but I'm scared to do anything else because everything I try that is water based stains the floor. Does anyone have any suggestions of how to clean this floor?

Have you thought about finishing the floors?

I have considered that, but since they are veneer ( thin layer of wood) I am worried that sanding them may ruin them altogether. They are beautiful floors but I can't clean them with anything waterbased and they are really looking very dingy!

Take a look here:

Veneer Care and Repair: WorkSpaces

The problem is that the floor needs to be kept dry and dog slobber is wet. Slightly soapy (dishwashing detergent) and dry COMPLETELY.

See if you can train dog to use his "throw rug" when he is in there with you.