Whenever I google it, I can only find abbreviated versions that negate characters like Kozeri, one of the sisters. I've read parts of it but I'm just having a hard time fully comprehending it. Any help would be appreciated.
There are texts to help you read the Tale of Genji. Puette has a reader's guide you can check out. When I read Tale of Genji, I used this free UNESCO source, which gives a great summary of each chapter. I also highly recommend you read Ivan Morris's The World of the Shining Price before you attempt to read the actual text, as it will explain to you everything you need to know about Heian court life.
You can find unabbreviated versions of Tale of Genji on Amazon. They're not that expensive.