I dunno how consistently “dramatic” The District was - it seemed to me that Nelson’s character was always going off on some goofy tangent before things got all serious and dark and preachy and it’s about the kids, dammit!
I nominate Maura Tierney, who got her big break on NewsRadio (admittedly as one of the more straitlaced characters) before moving on to ER.
Judd Hirsch (Taxi/Numb3rs)
Rick Schroeder (Silver Spoons/NYPD Blue)
Josh Charles (Sports Night/The Good Wife)
Chris Noth (Law & Order/Sex & the City/The Good Wife)
Bill Bixby (The Courtship of Eddie’s Father/The Incredible Hulk)
Brian Keith (Family Affair/Hardcastle & McCormick)
Gerald McRaney (Simon & Simon/Major Dad/Promised Land)
Jim Sikking (Hill Street Blues/Doogie Howser, M.D.)
Susan St. James (McMillan & Wife/Kate & Allie)
David Duchovny - the X-Files and Californication. (He was in other stuff too, of course).
Garret Dillahunt played evil men in three separate crime procedural dramas that I’ve seen - White Collar, Burn Notice and Life, the latter two roles being only for a few episodes, but the characters were significant - and was a one-off guest actor in lots of others too (I don’t know if he was always a bad guy, but I suspect he was). He was also the main terminator in both seasons of The Sarah Connor Chronicles. He was excellent at being a sociopath.
And then he became the loveable Dad (and Grandad) on Raising Hope.
Alyson Hannigan - Buffy, the Vampire Slayer and How I Met Your Mother (it occurs to me that if you just knew the titles and not the shows, you’d assume Buffy, the Vampire Slayer was a sitcom and How I Met Your Mother was a drama).
Actually, looking at wikipedia, poor O’Neil has been in like five failed TV dramas that either went one season or never got passed the pilot. I doubt they failed because of him, but he seems to be something of a kiss-of-death for dramatic TV.
Alan Alda - MASH and The West Wing
Candice Bergen - Murphy Brown and Boston Legal
Janeane Garofalo - The Larry Sanders Show and Criminal Minds: Suspect Behavior
Thomas Gibson - Criminal Minds and Dharma and Greg
John Larroquette - Black Sheep Squadron and Night Court
Matthew Perry - Friends and Studio 60 on the Sunset Strip
Robert Lyndsay, started his career in sitcom Citizen Smith, drama performances include roles in Hornblower, Oliver and much Shakespeare, has played the role of dentist Ben Harper in sitcom My family for the past 12 years.
His screen wife in My Family, Zoe Wanamaker, is mailnly known for her dramatic roles, appearing in Dicken’s adaptations, Dr Who and many, many others.