No Quidditch Cup is awarded this year; there is no mention of who wins the House Cup (1995)

Thanks to the Triwizard Tournament taking place at Hogwarts during Harry’s fourth year, the Quidditch games and the Quidditch Cup were cancelled.

“It is also my painful duty to inform you that the inter-house Quidditch Cup will not take place this year.”
— Albus Dumbledore (GF12)

The End of Term Feast was a subdued affair following the death of Cedric Diggory. The House Cup may have not been awarded because of this.

“When he, Ron and Hermione entered the Hall, they saw at once that the usual decorations were missing. The Great Hall was normally decorated with the winning house’s colours for the Leaving Feast. Tonight, however, there were black drapes on the wall behind the teachers’ table. Harry knew instantly that they were there as a mark of respect for Cedric.” (GF37)