Most people associate Thomas Dolby with the song "She Blinded Me With Science" from his EP Blinded by Science. It was used in the soundtrack to many TV-shows. But it isn't his only album or song.
This is "The Ability to Swing" by Thomas Dolby from the 1988 album Aliens Ate My Buick. I quite like it. It is a strange mix of rock, swing, with a few overtones of electronica.