How did west nile virus and sars cross contaminate?

You have to understand the connection here - birds.

SARS is an influenza like virus (coronavirus) that starts in birds (usualy chickens, although wild birds can be affected as well) that then mutates to cross into other species, like humans, pigs, ect. The odd thing about SARS is that it mutates into a "stable" state. Most common coronaviruses mutate so fast that you can't make a vaccine quick enough or that lasts from year to year Which is why most health professionals recommend that you get the flu vaccine every year. This is to compensate for the mutation.

West Nile virus is an arbovirus. Arbovirus are viruses that are insect related and in this case mosquetos are the cuplrit. Birds are affected as well as mammals. The problem in this case is that birds positive for West Nile can be hosts for the virus and when a mosquito bites it, then the virus can be transmitted by the now affected inscet. Mammals (including humans) are considered dead end hosts and do not "infect" the mosqueto.

as to your question. They are different viruses. Structurely they are different. They can contaminate the same person or bird at the same time, but they wouldn't be able to merge to form some new bug. It would be like trying to breed a dog to a cat. Wouldn't work unless you had some evil human making it happen