I'd like to add a band that came to me while I was in the shower just now (yeah, I know)
For those that don't know Soulwax
was/is a Belgium indie-rock band that produced three great rock albums. The two core members also had side projects as DJs and remixers and had a radio show on Belgium radio. They more or less are responsible for the (revival of the) whole mash-up thing in the DJ world. After releasing the three rock albums they more and more shifted their time to the DJing and producing part (they also performed electronic versions of their rock songs for some time as 'Soulwax night versions').
For many years they have not preformed with their rock band but only as DJs. Ironically one of their biggest hits is titled "Too many DJs" (everybody wants to be a DJ), the name of their DJ act.
I've seen their DJ set and their 'night versions' performance a few times but I've never seen the old rock show so I'd love to see them with their original rock band.