You could take the AQ Test, which is based on the Autism Spectrum Quotient. It was published by the Autism Research Center at Cambridge University. It doesn't give you a diagnosis, but rather suggests that some have more autistic traits based on their score. It measures autistic tendencies other than ones that would be considered a disorder, like most in the DSM.
One of my best friends has Aspergers. He isn't as socially inclined, but he's incredibly brilliant, with an IQ of over genius, and has remarkable spacial intelligence (the ability to take apart things in his mind).
Although I don't have any form of Autism, I do have the gene for spacial intelligence, and can assemble and dissemble things as large and complex as glass skyscrapers, although I am not nearly as intelligent as my friend. My father also has this ability, and it is thought that it was passed through his side of the family, as almost all of them majored in the sciences (see hyperlink). This is interesting, because spacial intelligence is not measured in a standardized IQ Test, which means it isn't officially recognized as a form of intelligence (due to it being kind of hard to measure). What's more interesting is that anyone who has strong spacial intelligence can tell you that it's based on examining parts and breaking them into smaller parts, much like the DSM cites that a person with Autism has:
"(d) persistent precoccupation with parts of objects."
This supports the Theory of Multiple Intelligences. This theory cites that there are different types of intelligence, and among those are not only Spacial but interestingly enough, Interpersonal, which, according to the DSM, Autistic people do not tend to have. It would make sense that there were different variations of the human race who were able to develop diverse skills, as the intelligences are widely varied. Neanderthals could have invented Spacial Intelligence, but could have lacked strong Interpersonal Intelligence. We could have inherited these genes from intermingling these variations.
Based on your theories of autism, I believe the AQ test is one of the best suited tests for determining whether different traits were passed through the human species. However, although I think this is an interesting theory, I wouldn't discuss this with someone who has Autism because he/she might find it offensive.