PA28 PLT HAD RWY INCURSION.

Narrative

A CURRENT STUDENT OF MINE WHO IS A PVT PLT IN NEED OF A FLT REVIEW; PURCHASED AN ACFT LOCATED IN MEMPHIS. BECAUSE HIS CERTIFICATE IS NOT CURRENT; HE ASKED IF I WOULD BRING THE ACFT BACK TO NASHVILLE; WHERE WE ARE LOCATED. BECAUSE THE ACFT IS A MEMBER OF THE PA28 FAMILY AND I HAVE CONSIDERABLE TIME IN OTHER ACFT IN THAT FAMILY; I AGREED TO FLY THE ACFT BACK; ALTHOUGH I HAD NO SPECIFIC TIME IN THE DAKOTA. ENRTE; THE TOP LATCH OF THE DOOR POPPED OPEN. IN ATTEMPTING TO CLOSE IT INFLT; WE UNLATCHED THE BOTTOM LATCH AS WELL. REALIZING WE WOULD NOT BE ABLE TO CLOSE THE DOOR INFLT; I REQUESTED RADAR VECTORS TO JACKSON IN ORDER TO LAND AND CLOSE THE DOOR. AFTER LNDG AT JACKSON ON RWY 20; I INADVERTENTLY MISTOOK THE XING RWY (RWY 11/29) FOR A TXWY. AFTER NOTICING MY ERROR; THE CTLR CLRED ME TO TAXI ON THE RWY. HOWEVER; I DID INITIALLY TAXI ONTO THE XING RWY WITHOUT CLRNC. ADDITIONALLY; UNTIL THE CTLR CLRED ME TO CONTINUE TAXIING; I DID NOT NOTICE I WAS ON A RWY. FACTORS THAT CONTRIBUTED TO THIS INCIDENT INCLUDED CONCERN OVER THE DOOR; MY STUDENT'S REACTION TO THE DOOR OPENING; WHICH WAS OVERBLOWN TO SAY THE LEAST; AND MY UNFAMILIARITY WITH THE ACFT; WHICH SERVED AS A DISTR. CORRECTIVE ACTIONS INCLUDED RECEIVING A CLRNC TO CONTINUE TAXIING ON THE RWY.