LAS TWR CTLR DESCRIBED NMAC WITH NUMEROUS FACTORS CONTRIBUTING TO THE CONFLICT AT APPROX 600 FT BETWEEN A GAR AND DEP FROM ANOTHER RWY.

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ACFT #1 WAS CLRED TO LAND ON THE RWY. A KING AIR PREVIOUSLY CLRED TO CROSS THE RWY INADVERTENTLY STOPPED ON THE RWY. GND AND I DIDN'T HAVE KING AIR ON FREQ. I ISSUED ACFT #1 GAR WITH STANDARD CLBOUT INSTRUCTIONS TO FLY RWY HDG MAINTAIN 3500 FT; UNTIL S OF THE FIELD. USUALLY THE CLB HAPPENS ABEAM THE CTL TWR; BUT DURING THIS GAR; A CESSNA HAD STRAYED INTO THE DEP CORRIDOR CONVERGING AT 4200 FT. AFTER ISSUING ACFT #1 GAR; I WAS ADVISED BY THE INTERSECTING RWY TWR CTLR OF HIS DEP ACFT #2. I HAD PREVIOUSLY ADVISED THE TWR CTLR OF MY GAR. THE DEP WAS A B752 (ACFT #2). (WHILE I MENTIONED 'INTERSECTING;' ACTUALLY WITH CURRENT RWY CONSTRUCTION; MGMNT ADVISED US TO TREAT THEM AS 'NON INTERSECTING' RWYS.) THE OTHER TWR TOLD ACFT #2 TO STAY LOW; BUT WITH A CESSNA RUNNING 'AMOK' THROUGH THE DEP CORRIDOR; I COULDN'T CLB OR DSND OR TURN L (WAKE TURB). I IMMEDIATELY ISSUED A TFC ALERT TO ACFT #1; ADVISED ACFT OF ACFT #2 LOCATION; DIRECTION; AND ADVISED ACFT #1 TURN TO AVOID. NO RESPONSE. I RE-ISSUED THE TFC ALERT. WITHOUT ANY PROCS IN PLACE TO ADDRESS; I QUICKLY DETERMINED WITH SUCH CLOSE PROX TO EACH OTHER; CONVERGING AT A HIGH RATE; THAT IF I ISSUED A R HDG TO ACFT #1 WITHOUT ACFT #1 SEEING ACFT #2 AT A STANDARD RATE OF TURN; THE 2 ACFT HAD THE POSSIBILITY OF JOINING. ACFT #1 RESPONDED IMMEDIATELY AFTER MY SECOND CALL STATING A R TURN. AFTER ACFT #1'S TURN; I ISSUED A THIRD TFC ALERT FOR THE CESSNA 1 O'CLOCK POS; 1/2 MI; 500 FT ABOVE; NBOUND; AND GAVE ACFT #1 A HDG TO DIVERGE FROM ACFT #2 AND RESTATED 3500 FT FOR THE CESSNA. AFTER COORD WITH DEP; I LEFT ACFT #1 ON THAT HDG AND ONCE CLR OF THE CESSNA; 7000 FT AND TOLD TO CONTACT THE DEP CTLR.