"The shoot-out scene that initiates Morpheus's rescue, and which complements the earlier dojo fighting sequence, is set to the Propellerheads' electronica-influenced "Spybreak""
quoted from http://www.latrobe.edu.au/screeningthepast/fir strelease/fr_18/DSfr18a.html
the version used in the dojo scene is "spybreak"(short)
The music played in during the scene in the gym is called 'Leave You Far Behind' by 'Lunatic Calm'. No I've never heard of them either.
The music played during the shootout in the lobby is the superb 'Spybreak! (short one)' by the 'Propellerheads'.