TER General Board
Well, the unfortunate truth is that the technology IS available to narrow it down more than "non-specific viral crud." You could have had tests to identify infection with various adenoviruses, coxsackieviruses, parainfluenzaviruses, rhinoviruses, etc., probably at $$$ a pop (pun intended), but the results would return a few weeks later after you were well and couldn't affect your "treatment", because there really IS no treatment for these self-limited infections other than rest and chicken soup and aspirin and antihistamines. So, nobody does such testing.
Sometimes the CDC will sponsor testing in a community to learn what viruses are currently causiing "non-specific viral crud", and it's valuable epidemiologically, but not useful to the individual sufferer.
When the virus at issue is a real worry, the CDC does all KINDS of interesting monitoring; e.g., counting dead crows in agricultural areas and looking for infection in "sentinel chickens" to monitor West Nile Virus in the Western U.S.
More than once virtually the entire commercial supply of chickens for food have been destroyed in cities in China because of potentially dangerous Influenza epidemics in the chicken population
I got whacked by "non-specific viral crud" about 10 days before a business trip that was scheduled to include an overnight with a delightful lady. As I lay in bed dieting for 3.5 days, my only real concern was whether I'd be well enough for the liason and coughing infrequently enough not to scare her away 
Things worked out pretty well!