|What OtheHill was referring to was more an more laptops of dubious provenance.|
Dell could work out where the laptop was sold from the serial number but that would take some research by them, whereas the owner should be able to find out that information very quickly. There is a service tag no on the laptop but that will be tied to the original owner.
You have no choice but to contact the original owner. Dell are not going to provide a warranty if there is the slightest suspicion that the current owner is not the legitimate one. Do you have a receipt, a bill of sale or something to prove that you are the legitimate owner of the laptop.