Passengers Begin Disembarking Disabled Carnival Cruise Ship in Mobile, Ala.

Feb. 14, 2013 — -- The ordeal of the disabled Carnival Triumph cruise ship carrying 4,000 passengers and crew appeared to be almost over, with people starting to disembark in Mobile, Ala., after days at sea without power in often squalid conditions.

After the ship arrived at port around 9:30 p.m. local time (10:30 p.m. ET), Carnival president and CEO Gerry Cahill praised the ship's crew and told reporters that he was headed on board to apologize directly to its passengers.

Passengers appeared to begin disembarking around 10:15 p.m. CT (11:15 p.m. ET).

The Carnival Triumph departed Galveston, Texas, Thursday and lost power Sunday after a fire in the engine room disabled the vessel's propulsion system and knocked out most of its power.

After power went out, passengers texted ABC News that sewage was seeping down the walls from burst plumbing pipes, carpets were wet with urine, and food was in short supply. Reports surfaced of elderly passengers running out of critical heart medicine and others on board squabbling over scarce food.

"I know the conditions on board were very poor," Cahill said. "I know it was very difficult, and I want to apologize again for subjecting our guests for that. ... Clearly, we failed in this particular case."

It could take up to five hours to get everybody off the huge ship.

"Inside the terminal, there's also warm food available," said Terry Thornton, Carnival's senior vice president of marketing. "There are blankets, there are cell phones and refreshments available for the guests that need that or want that assistance.

Passengers will have the options of boarding buses to Houston or Galveston, Texas, about seven hours away, or New Orleans, about two hours away, officials said.

"We have gotten our guests back to land," Cahill said. "Now, we need to get them home. ... The full resources of Carnival are working from here to get them home as quickly as we possibly can."

At an earlier news conference this afternoon, Thornton said that anyone with special needs and children will be the first to get off the boat. He said the company's No. 1 priority is to make the process as "quick, efficient and comfortable" for guests as possible.

"There are some limitations. We know that up front," Thornton said. "The ship still does not have power. We only have one functioning elevator aboard."

Click here for photos of the stranded ship at sea.

The passengers were achingly close to port about noon today as the ship began to enter the channel and proceed to the cruise terminal. At 1 p.m., the lead tow boat had a tow gear break, so a spare tug boat that was on standby had to be sent in to replace it.

But once the second tug was in position and the lines were re-set, the towing resumed only briefly before the tow line snapped.

"We had to replace that tow line, so the ship did not begin progressing back into the cruise terminal until 2 p.m.," Thornton said

Passengers desperate to get off the vessel waved at media helicopters that flew out to film the ship and passenger Rob Mowlam told ABCNews.com by phone today that most of the passengers on board were "really upbeat and positive."

Nevertheless, when he gets off Mowlam said, "I will probably flush the toilet 10 times just because I can."

Mowlam, 37, got married on board the Triumph Friday and said he and his wife, Stephanie Stevenson, 27, haven't yet thought of redoing the honeymoon other than to say, "It won't be a cruise."

Alabama State Port Authority Director Jimmy Lyons said that with powerless "dead ships" like the Triumph, it is usually safer to bring them in during daylight hours, but, "Once they make the initial effort to come into the channel, there's no turning back."

"There are issues regarding coming into the ship channel and docking at night because the ship has no power and there's safety issues there," Richard Tillman of the Mobile Bay Convention and Visitors Bureau told ABCNews.com.

When asked if the ship could be disembarked in the dark of night, Tillman said, "It is not advised. It would be very unusual."

Thornton denied the rumors that there was a fatality on the ship. He said that there was one illness early on, a dialysis patient, but that passenger was removed from the vessel and transferred to a medical facility.

The U.S. Coast Guard was assisting and there were multiple generators on board. Customs officials were to board the ship while it was being piloted to port to accelerate the embarkation, officials said.

Carnival Cruise Ship Delayed by Snapped Tow Line

After eight days at sea, many of them without power, the ship's owners have increased the compensation for what some on board are calling the vacation from hell.

All 3,143 passengers aboard the 900 foot colossus, which stalled in the Gulf of Mexico after an engine room fire early Sunday, were already being given a full refund for the cruise, transportation expenses and vouchers for a another cruise. Carnival Cruise Lines is now boosting that offer to include another $500 per person. Gerry Cahill, president and CEO of Carnival Cruise Lines, announced the additional compensation Wednesday.

"We know it has been a longer journey back than we anticipated at the beginning of the week under very challenging circumstances," he said in a statement. "We are very sorry for what our guests have had to endure. Therefore, in addition to the full refund and future cruise credit already offered, we have decided to provide this additional compensation."

Carnival added that it has canceled a dozen planned voyages for the Triumph and acknowledged that the crippled ship had been plagued by other mechanical problems in the weeks before an engine-room fire left it powerless in the Gulf of Mexico.

ABC News flew over the ship providing the first aerial views of the ship showing curious passengers gathering at the rails, looking up at the ABC News plane. It also seemed from the air that deck chairs had been turned into beds.

"[There are] no showers. The smell's terrible. We are camping on deck," passenger Ann Barlow told ABC News.

Mary Poray, whose 12-year-old daughter Rebekah is traveling on the Triumph, teared up when shown images of the ship's deck.

"I just need to know that she's OK," Poray said. "The worst part was when she said, 'Mommy, I'm afraid I won't ever get to see you again."