Why not use SDS-PAGE as a method to detect viruses?
Put simply, the answer is that you could seek to detect viral proteins, but because these proteins would be very minor components of your sample, you would have to use an immunoblotting technique to detect a specific viral protein. While immunoblotting is quite a sensitive technique, I think its fair to say that it can be technically demanding. In contrast a PCR reaction is exquisitely sensitive and is fairly robust. PCR is also technically more staightfoward because DNA is generally easier to work with than are proteins. 

Before the advent of PCR, immunoblotting would have been the method of choice.