I'm looking for older 90s and early 00s underrated dramas. No comedy please.

Aishiteiru to Ittekure-Japanese drama about a man and a woman fall in love, but the male lead is deaf.

Sandglass-Korean drama about two friends who fall for the same girl, but takes place during the 1970s and 1980s (lot of changes and a lot of history during those periods especially the 80s).

Bokura no Yuuki- Japanese drama about a guy who goes to a city to volunteer for an earthquake strike effort. But once he gets there, it is city lockdown and the town is not what he expects.

Kamisama Mou Sukoshi Dake- Japanese drama about a young girl who has contracted HIV. 

MARS- Taiwanese drama about an introvert girl with a chip on her shoulder and a popular male student with a chip on his shoulder who connect and fall in love (Trigger Warning: Rape shown, but not too explicit, but not a fan, don't watch!!!!)

Kurosagi-Japanese drama about a con-artist who targets professional con-artists. It is like a modern Robin Hood.

Silence- Taiwanese drama about a girl who becomes mute after an accident and meet a rich man who has cancer ( warning: there are a lot of flashbacks). 

I noted that you have watched Winter Sonata.. you may want to try the other three of this season-themed Endless Love tetralogy?

Also (some are fun, lighthearted, but not slapstick comedy, and have thought provoking and heart tugging moments):

  • Jewel in the Palace (2003): One of the earlier popular and well-liked Kdrama in East and South Asia, and a quality production based on the true story of the first female royal physician of the Joseon Dynasty.
  • Full House (2004): Pioneer of the Korean rom-com genre and the many rom-com clichés of rich male lead, boss-employee relationship, contract marriage, and bickering couple, and has since been remade in many other Asian countries.
  • The Last Breakthrough (2004): HK TVB anniversary drama and a gem for medical drama on medical professionals volunteering as doctors without borders at feudal, resource- and disease- stricken areas providing medical humanitarian assistance for the needy locals. It is also on medical ethics, on crossing the doctor’s line to help patients and at the same time on finding the real meaning of life, family and friends, and living life to the fullest and without regrets. More in my review.
  • Beach Boys (1997): Fun, hilarious, heartwarming yet healing slice-of-life Jdrama of 2 city guys who were both lost in their own life, escaping to a beach B&B homestay, building deep friendship with each other and folks at the homestay and finding purpose and direction in life. A good summer watch.

Perhaps you can find other interesting ones here: 

Btw i clicked in from the Recent Discussions, and didnt realise this was posted under Korean category. Nevertheless, the other two non-Korean dramas are really good and worth checking out!