Visitors to the Palace, as it should be, go in raptures in front of the two most illustrious surviving rooms of the Norman era: the Palatine Chapel and the King Ruggero Room (this feeling is also mine, having visited the Palace for the second time after 45 years).
What escapes most - and which in my opinion is not even adequately remembered in the panels illustrating the Palace halls - is that these two highlights are what survives many destructions and looting in the same or subsequent age than that of the two most illustrious halls (12th century). Among the destructions, the looting in the revolt following the conspiracy by the nobles so-called by Matteo Bonello (1160) stands out in the first place; then the plundering of the palace by Henry VI of Hohenstaufen (holy Roman emperor and father of Frederick II) in 1194; finally, the further destruction caused by the so-called "Vespers" revolt (1282).
Following these repeated devastations, it's understandable that the Palazzo, an amazing work celebrated by many 12th century witnesses, has fallen into decline and has gradually ceased to be the representative center of royal power. It's revealing, for example, that the Aragon dynasty, ruler of Sicily after 1282, established its residence not here, but in the illustrious, but much less grandiose building called Steri (in today's Piazza Marina).
The palace returned to being the center of political power in Sicily only since the middle of the sixteenth century, with the Spanish viceroys (but at that time Sicily was far from having the function it had in the twelfth century in Europe and in the Mediterranean). Under the viceroys, therefore, the demolition of the dilapidated parts and the construction of new wings took place (including what is currently the "Hall of Parliament" or "Hall of Hercules").
This explains why, despite its name (which, moreover, was given to it recently, in the twentieth century), the Palazzo dei Normanni now has a prevailing early modern architectural look, in which the medieval parts appear as residues. Subsequent changes see the insertion of the current courtyards and the monumental staircase, through which visitors pass today.
We must therefore resort to the imagination to get the sense of halls and furnishings congruent with the two splendid elements that we still admire today. The descriptions of the palace in the twelfth century can help the imagination (for such description a summary is in a paper by the medieval art historian Ruggero Longo  freely available on the web).