* Sun begins to shine, but flood waters still dangerous
* Storm dumped more than 2 feet (61 cm) of rain over some areas
* Two deaths blamed on Debby, two others may be storm-related (Adds body found in river, updates storm status)
By Michael Peltier
TALLAHASSEE, Fla., June 27 (Reuters) - The remnants of Tropical Storm Debby moved out into the open Atlantic on Wednesday and rains finally eased over Florida but the state was struggling to clean up the soggy mess left behind.
In Debby's wake were flooded homes and businesses, roads under water or cratered with sinkholes, and overflowing rivers that sent thousands fleeing for higher ground.
Emergency managers said it was too early to gauge the extent of the damage. About 11,000 customers were without electric power in 39 counties on Wednesday, down from 29,000 on Tuesday.
The storm deluged parts of central and northern Florida with more than two feet (61 cm) of rain as it hovered in the Gulf of Mexico and cut across the peninsula. It was downgraded to a tropical depression when its winds died down on Tuesday night.
By Wednesday afternoon it was just a disorganized mass of thunderstorms out in the Atlantic, falling apart as it sped away from the Florida coast.
"Rainfall associated with Debby will continue to diminish across the Florida Peninsula today," forecasters at the U.S. National Hurricane Center in Miami said.
Two Florida deaths were blamed on the storm and medical examiners were trying to determine whether two others were storm-related.
A central Florida woman in Polk County was killed when her car hydro-planed on a flooded road and a woman in neighboring Highlands County was killed when a tornado wrecked her home, a spokeswoman for the Florida Division of Emergency Management said.
A man died after his canoe capsized on Lake Dorr in the Ocala National Forest a few hours after Debby made landfall on Tuesday, and medical examiners were still investigating whether his death was related to the storm.
On Wednesday, Pasco County Sheriff's waded into flood waters around the Anclote River to recover the body of a man in his 40s.
"At this point it's really too early to tell what the cause of death was," sheriff's spokesman Doug Tobin said.
Torrential rains caused the Anclote to rise from nine feet (2.7 metres) before the storm to major flood level of 27 feet (8.2 metres) on Tuesday. The flood waters had receded a little on Wednesday but still lapped dangerously over surrounding roadways and had a strong enough current to sweep people away, Tobin said.
"Even though it's sunny out we're still urging people to use extreme caution in crossing roads that have water flowing over them. They are still extremely dangerous," he said. (Writing by Jane Sutton; Editing by Vicki Allen and Eric Walsh)