1997 MIT Mystery Hunt Puzzle 1 Solution

Perhaps the most obvious starting point is the 8th item. The first and third words start with the same two bigrams, and due to the way the code works, it's possible and reasonable to assume this might consist of the same word three times. This is Girls! Girls! Girls!, the title of an Elvis Presley film. You can then match the remaining items to other Elvis film titles by length (with dummy letters shown):

PL EC KA DA = TICKLE ME
LR KN SH OG AE QS CQ =JAILHOUSE ROCKX
FJ QM LD YR KW KW = BLUE HAWAIXIX
VH PG KA PA PO FJ XK = DOUBLE TROUBLEQ
BA ML LK AM HM HP JH LZ = FRANKIE AND JOHNNY
LK CV BH KG PO BH HG = KISXSIN' COUSINS
FO YT RY YT HP XQ = STAY AWAY, JOEX
BN AJ BS BW HF BN AJ CV = GIRLS! GIRLS! GIRLSX!
SK ML CM TS LD RB QY = CHANGE OF HABITX
TR EM RH CD LD YR KW LR HG LT KA = PARADISE, HAWAIXIAN STYLE
LP LD QT QR KM RM UT OL RX PD HA BG RL EP = IT HAPQPENED ATQ THE WORLD'S FAIRQ
NK XD YF LP LF AK HO AM NK QY LF XK = LIVE A LITTLE, LOVE A LITXTLEQ
OL AQ DP PG KA PB OL BN AJ FD HM SH YP US AQ KH UP LP = THE TROUBLE WITH GIRLS (AND HOW TO GET INTO IT)
DP OG LY SP OU = ROUSTABOUT

These can be used to deduce the Playfair square:

DREAM
SBCFG
HIKLN
OPQTU
VWXYZ

The key which appears in the first two lines, before the other alphabetized letters, is DREAMS, which is also the answer.