(Disclosure, I may receive a small referral fee when you make a purchase through this links on this post.)
Well you are in luck. Amazon signed a deal with PBS Kids to be the exclusive premium subscription service on their Prime video service. This is an agreement that will span multiple years. For people with Amazon Prime membership, you will be able to watch PBS Kids on the PC through www.amazon.com/primevideos through a web browser or use the Amazon Video App. I just gave this a try and a quick search yielded 53 TV show results! Some are individual videos and some are entire season series so the actual videos are much much more.