It doesn't seem that they got much financial assistance from the government. Almost everything is owned by various co-ops and as for a turbine breaking, the Danes have heard of warranties and insurance.
Here's a rather old report on the insurance of wind turbines:
http://www.imia.com/downloads/imia_papers/wgp05_1999.pdfThe 10 year report (
http://energiakademiet.dk/images/imageupload/file/UK/RE-island/10year_energyrepport_UK.PDF) should have all the answers about funding. A quick glance shows that less than 2 million EUR in gov't funding for various district heating plants, only until 2001 and the wind turbines are funded / owned by a mix of the municipality, private investors, farmers and local citizens co-ops. Since the turbines produce more than the island consumes, they have electricity to sell.
I would be surprised if the payback is as low as 7 years on the turbines but it looks to be well below the expected lifespan so they should make money while getting free electricity.
http://energiakademiet.dk/default_uk.asp 
