BOEING 727 (NORTHWEST FLT 354) & USAF EC-135 (SLUM 51) WERE INVOLVED IN A NR COLLISION AT FL 330. THE MISHAP OCCURRED AS FLT 354 WAS ENE BND ON J-158 & SLUM 51 WAS FLYING ON A RADIAL-DISTANCE (R/D) FLT PLN, FLYING BTN R/D PTS SOUTH OF J-158. AS SLUM 51 APCHD ITS MOST WESTERN PT, THE CREW REQD A RGT TURN TO A R/D PT THAT WAS NOT THE NEXT LISTED PT ON THEIR FLT PLN. THE TRAINEE CTLR (T/C) DIDN'T REALIZE SLUM 51 WAS REQG A ROUTE CHG, BUT THOUGHT THE FLT WANTED TO TURN BACK EAST TO THE NEXT FILED R/D PT WITH A RGT TURN (INSTEAD OF A L TURN AS PREVIOUSLY DONE). THE T/C REPLIED, 'UNABLE RGT TURN, MAKE A LEFT TURN.' THE INSTRUCTOR HEARD THE REQ, BUT THOUGHT THE T/C'S REPLY WAS DISAPPROVAL OF A ROUTE CHG. AS THE CTLRS TURNED THEIR ATTN TO OTR (HVY/COMPLEX) TRAFFIC, SLUM 51 CONTD A 270 DEG L TURN (TO NORTH) & CONVERGED WITH FLT 354. THE 9020 (PRIMARY) COMPUTER WAS INOP; THE DARC (BACKUP) COMPUTER HAD NO CAPABILITY OF DISPLAYING PROJECTED ROUTES OR PROVIDING CONFLICT ALERT. NO FLOW CTL RESTRICTIONS WERE IN EFFECT TO RDC THE AMOUNT OF TRAFFIC.