Rick Dow and his wife, Cecilila, took a trip on the ship at the end of January.
Not long after the ship set sail, plans changed.
"They announced they have a problem with the propulsion system and couldn't reach speed they normally use, so we couldn't go to the further destination," Dow said.
Dow said the cruise was cut short, which meant they didn't get to go to Cozumel.
"There were a significant number of people who were really upset," Dow said.
Dow said many customers weren't happy with the "compensation" they received.
"To miss half your destinations and be given a token $50 credit for that ... just didn't sit well with a lot of people," Dow said.
KPRC Local 2 asked Carnival about the previous problems.
"Carnival Triumph previously experienced an electrical issue with one of the ship's alternators," a statement from the company read. "Repairs were conducted by the alternator supplier and were fully completed on February 2. There is no evidence at this time of any relationship between this previous issue and the fire that occurred on Feb. 10."
What rights to passengers have if their cruise doesn't go well?
"Their rights are limited," KPRC Local 2 legal analyst Brian Wice said. "When you board the ship, after having purchased a ticket, you are not going to be able to recover all of that much."
Wice said when a passenger boards a ship, they have entered into a contract with the carrier. That contract limits the company's liability.