I found this on a site...

" Peonies are not for every climate. They really need a cool climate, with some frosts. The usual reason for non flowering is that you are in too warm a climate and/or the peony has been planted too deep. The top of the bud should be no greater than 4cms under the ground. Any deeper and it may not flower. Peonies need frost or they will not set flower buds. "

Planted too deep??
Have you mulched the soil and therefore buried the original one too deeply??

I know they often won't flower for a year after they have been moved- could that be the problem with the new ones???

Or...just too mild this winter in an already sheltered spot????