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Out of all the dramas that I have watched, only 1 wasn't a Japanese drama. Due to finally finding a band that I really love, I have decided to start watching Korean dramas. I would really love some help to get me started so if I can get some recommendations from the following genres/descriptions, it would be appreciated.

I like watching shows about:

Detectives: especially about high school kids like "Tantei Gakuen Q", "ST Aka to Shiro no Sousa File" or with a Sherlock feel like "Kindaichi Shonen" or "Rinsho Hanzai"

Delinquents: shows either like "Majisuka Gakuen" and "Shiritsu Bakaleya Koukou", or like "Gokusen"

I don't mind if any of the above have a romantic sub plot (usually enjoy it, especially when there is comedy as well) but I don't really want any that is just a romance genre.

Basically if any of the shows are like any of the ones that I have rated high already then I will probably enjoy it. 

I will take any other recommendations if it is one you enjoy or if it is a good place to start with kdrama. 

Since I'm not sure if these subjects show up in Korean dramas like in Japanese dramas, I would like it if someone lets me know. Thanks!

So far, I've only seen Gokusen and Tantei Gakuen Q from what you said. I enjoyed them when I was younger too. I think the latest trend and what's considered a quality drama in the K-drama industry is a bit different from those ones. Give them a try and you'll find the charm of Korean dramas as well :)) You can also read my highly recommended dramas on my profile page. I wrote the reasons why I recommend them there.

These will probably be good for a starter:
Signal - http://mydramalist.com/13239-signal
City Hunter - http://mydramalist.com/1702-city-hunter-2011
Chief Kim - http://mydramalist.com/20340-chief-kim
Healer - http://mydramalist.com/10814-healer
You're All Surrounded - http://mydramalist.com/9288-youre-all-surrounded
School 2013 - http://mydramalist.com/5571-school-2013 - for the "delinquent" category, this one matches the best.
Hi! I'll recommend these dramas:

Hello Monster/I Remember You
Nightmare Teacher (Webdrama)
Bring It On, Ghost

I remember You
Kill me, heal me
Suspicious Partner (still airing)
The K2
W: Two Worlds
I haven't seen nothing quite like what you mentiones, but since you said you like detective dramas and I saw in you list you have some suspense dramas rated with 10, watch:

I hear your voice

And also I know your asking for kdrama recommendations but I saw you ahve "Maou" in your PTW, so I want to recommend you watch it is an excellent drama!