The BBC's Joseph Guyla Delva, who accompanied a team from the UN's peacekeeping mission as they flew by helicopter over the area, says many houses have been damaged or destroyed, and that authorities estimate 80% of Gonaives' population has been affected by the storm.
Senator Yuri Latortue, who represents the city, said about 200,000 people there had not eaten for three days.
The UN aid shipment included bottled water, water-purification tablets, high-energy biscuits, cooking oil and rice.
UN peacekeeping soldiers aimed to distribute the biscuits and water within hours to emergency shelters where 40,000 people are marooned.
Prospery Raymond, from Christian Aid, said farmland had been flooded and the loss of crops was set to push food costs higher.
"The whole of the Artibonite valley has been submerged, which is where 80% of Haitian rice is grown. Rice crops were destroyed near the point of harvesting, which can only put the price of this staple food even further out of the reach of many families."
"There is no food, no water, no clothes," Arnaud Dumas, a pastor at a Gonaives church, told the Associated Press news agency. "We haven't found anything to eat in two, three days. Nothing at all."
An AP reporter in the city said safe drinking water was in very short supply, and fetid carcasses of drowned farm animals were strewn in soupy floodwaters.
Johnny Auguste, a shepherd from the south-western city of Miragoane, told the BBC that things were "very bad".
"In my area, I'd say about 20 people have died. There's a lot of flooding and the people have nothing to eat. The people feel really bad because there's no food, there's no work, the people don't know when this is going to stop."
After hitting Haiti, Hanna moved north, past the edge of the Bahamas. It is now expected to reach the Carolinas on the US east coast early on Saturday.
Tropical storm and hurricane warning from BBC weather
There are fears Hanna could become a hurricane by the time it hits the US, but the storm's uncertain path means officials are holding off ordering an evacuation.
However, a hurricane watch is in place in North and South Carolina. Some residents have already moved boats and booked inland hotel rooms.
Meanwhile Hurricane Ike could pass close to northern Haiti before taking aim at south Florida, Cuba or the Gulf of Mexico next week.
It is almost certain to dump more rain in Haiti's Artibonite Valley, whose rivers funnel into Gonaives.
"The soil is completely impregnated with water and there is no way for the rivers to take more water," Max Cocsi, in Gonaives with Doctors Without Borders, said.
Ike has weakened slightly into a Category Three hurricane in the open Atlantic, the National Hurricane Center says, but it remains "dangerous".
A team from the American Red Cross flew over Gonaives
Mr Boutroue, the UN co-ordinator for humanitarian aid in Haiti, told the BBC that aid workers face "a lot of difficulty trying to respond" in the wake of Hanna.
"In Gonaives alone we have some 70,000 people in shelters, and around 250,000 around Gonaives City need our assistance and that of the government, and throughout the country I would say around up to 600,000 people might require our assistance."
The storms, Mr Boutroue said, were likely to deepen further Haiti's already extreme poverty.
"That potentially means more instability unless we can ensure an adequate response," he said.
The International Federation of Red Cross and Red Crescent Societies has also launched an appeal, asking for $3.4m dollars in aid.
Haiti was first drenched by Tropical Storm Fay, before Hurricane Gustav wreaked havoc last week, with torrential rainfall over heavily deforested and hilly terrain causing floods and mudslides.
Earlier Hanna was also blamed for two deaths in Puerto Rico.
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