What was found
AFTER PUSH BACK, DURING THE AFTER START FLOW WE GOT ON THE PFD 2 A: 1. HDG FAIL, 2. WX FAIL, 3. TERR FAIL, & 4 TCAS FAIL MSG. AFTER RUNNING THE HDG FAIL CHECK LIST (4.18) AND DOING THE SPGRG AHRU RESET, MX REQUESTED TO RETURN TO GATE. DURING THE TAXI BACK TO THE GATE, WE NOTICED AN ELECTRICAL BURN SMELL IN THE COCKPIT. REMOVED FROM SERVICE. PERFORMED THE AIR CONTAMINATION CHECKLIST, DETERMINED THAT ELECTRICAL SMELL WAS EXTERNAL OF AIRCRAFT. POWERED OFF AND ON THE AIRCRAFT, NO FAIL MESSAGES OCCURRED. PERFORMED OPS TEST OF THE WEATHER RADAR IAW Q400 AMM 34-41-00-710-804, TEST GOOD. PERFORMED OPS TEST OF THE EGPWS IAW AMM 34-42-00-710-802, TEST GOOD. PERFORMED OPS TEST OF THE TCAS IAW AMM 34-43-00-710-801, TEST GOOD. PERFORMED OPS TEST OF THE AHRU CONTROLLER IAW MTC 6342102, TEST GOOD. PERFORMED AHRU COMPUTER OPS TEST IAW MGTC 6342101, TEST GOOD. PERFORMED HGS OPS TEST IAW MTC 6343510, TEST GOOD. FAIL MESSAGED DID NOT RETURN. NO OTHER DEFECTS NOTED. AIRCRAFT STATUS REMAINS CAT III. COCKPIT PLACARD READS CAT III. MTX CONTROL NOTIFIED. NO PARTS REPLACED. AIRCRAFT RETURNED TO SERVICE.