Once you get the first board off (sawzall the nails under) the rest should pry up. Check out "deck wrecker" on Amazon - a big pry bar - though you could use a long plank to get similar leverage.

Hi, Thank you for your response! When you say "sawzall the nails under" do you mean to cut off nail heads with sawzall? We don't have a sawzall. Would some other kind of blade work?

The key is getting the the first board up. Once this one is up you can pry up the rest using the first board as a lever (or some other long pry bar). Not sure of your access - I was suggesting for the first board cutting the nails from underneath to free it up. Maybe this one could be pried up? Or cut the nails from underneath just using a hacksaw blade. Or carefully pull the nails from the top using a wonder bar or similar. Or the first board is sacrificial. After board one pry the rest up.

Another thought is to flip the boards - the underside may be in much better shape. (Should you damage one during demo)

OK, thank you for more info! The deck is low and unfortunately there is no access from underneath. We'll look into wonder bar. Thank you also for the idea of slipping the boards!