The below is the one everyone in this thread is recommending.
http://www.jreast.co.jp/e/nex/
Also you can take a bus
https://www.limousinebus.co.jp/en/bus_services/narita/shinjuku.html
The closest to Kabukicho is Shinjuku Expressway Bus Terminal (the last stop).
If you cannot cancel the Keisei ticket, I recommend you to get off at Nippori - the first stop after Narita Terminal 2. The journey time is about 35 to 40 minutes. Then change trains to JR Yamanote Line. You need to buy a ticket (costs 200 Yen) or buy a Suica card (something like an Oyster card for London Underground) from a ticket machine after exiting from Keisei's Nippori station. The Yamanote line's platforms are at far end (platform 10 and 11) from Keisei's exit. Take a train colored sliver with yellow-green lines above and under the windows. It's a loop line so you can take a train for either direction, but a north-bound train (platform 11) will bring you a tad faster to Shinjuku. The morning rush hour usually ends around 9am.
You may be able to take a taxi from Keisei Ueno - it costs around Yen 3000 to 3500 to Kabukicho.