Kentuckiana Digital Library is a website of digital collections from all over Kentucky. According to their website there you can "find over 80,000 photographic images, 100,000 newspaper pages, 230,000 book pages, hundreds of oral histories, and maps documenting the history and heritage of Kentucky."
Kentucky Vital Records Indexes This will link you to digital images of vital records online available through the University of Kentucky. The records were acquired from the Kentucky Office of Vital Records. They are for fairly recent years but it might be of use to someone just getting started. You might also want to read their explanatory notes if you have trouble finding who you are looking for. It explains a lot about how well record keeping was done.