"Dead money" will still work the same way w/r/t to cap figures, but does not figure into calculations of cash figures.
I don't know what the exact salary floor was in 2009, but the cap was $127 million and the
Chiefs were paying $82 million, or 64% of the cap, in actual payroll. 7 teams were paying less than 75% of cap value in actual payroll. All but two of those teams were in the bottom half in terms of cap number -- so it's not like their actual payroll was being constrained by 'cap hell.'
Even if the cap would have been dropped to $120 under the new rules, with a cash floor close to 100% of the cap, as reported, that's almost a quarter of the league that would need to increase actual payroll by $25-40 million.