Plants that are in full sun will leaf out earlier than those in partially sunny areas. But no matter where it is planted, one of rose of Sharon's (Hibiscus syriacus) other disadvantages is that it is susceptible to winter injury and twig die-back. If the branches are still limber and still showing green when you scratch off a bit of the top gray bark, it is possible they receive less sun and are still catching up.
Select a random branch tip on the rose of Sharon shrub that is about 1/4 inch in diameter and bend the tip back with your hand. If the rose of Sharon is dead, the branch tip will break and the inside will be brown and dry. If the rose of Sharon is alive, the branch will bend easily, eventually split and the inside will be green and moist.
Scratch about 1/2 inch of the bark back on a random branch with the edge of a knife or your fingernail to expose the cambium layer just underneath the outer bark. The rose of Sharon is dead if the bark's under layer is brown and dry. The rose of Sharon is still alive if the bark's under layer is green and moist.
Look at the rose of Sharon for signs of life throughout the season by looking closely at its branches for new growth, such as emerging buds and leaves. Watch for new shoots that may emerge at the base of the rose of Sharon.
If the limbs are brittle, it is likely they have died from winter kill. I would wait a bit longer. If they absolutely refuse to bloom, they should be pruned off at ground level for cosmetic reasons if no other reason. A moderate amount of fertilizer might also be beneficial at that point.
Caring for your Rose of Sharon:
The Rose of Sharon needs moist and well-drained soil. Apply a single layer of compost under the outermost branches of the shrub during the spring. To enhance blooming and promote larger blossoms, prune the shrub each spring, retaining only two to three buds on each branch. Remove dead, diseased and damaged branches constantly to help the blooms flourish. Prune away up to one-third of the oldest branches to rejuvenate the Rose of Sharon. Look for thicker stems, cutting those branches at the base. These will be the future of your beautiful shrubs.
Annual pruning back will result in increases shoot vigor and larger flowers. Your shrubs appear to be a little "twiggy" and perhaps have not be kept pruned back. Removing some of the oldest shoots annually will encourage fresh new growth from the bottom and also keep your shrubs at a more modest size.