I'm no expert, but I have experienced a similar situation after overwintering. Most of my roses that do that seem to recover nicely by mid-summer.

Alfalfa pellets have an almost magical ability to encourage new growth; but right now the rose is probably pretty busy replacing its root system. Next season will tell!

I raved on and on about a rose I have had for years that has thrived despite being completely ignored. I said it was First Prize but today at nursery I discovered it was the climber America. An amazing specimen - disease free and ever blooming and loves neglect. Get one - you will be delighted!

A few questions -

Is it grafted? If so, is it planted deep with the graft 2" inches below soil?

Can you prune the dead stuff way back to open up the crown?

If it's own root OR grafted and planted deep and you prune back the dead stuff, it should easily send up new shoots to fill in the shrub. It may not do much until next season, though, since it has to re-establish it's roots this year.

If it's grafted and not planted deep, you may want to prune off the dead stuff and consider re-planting it deeper in the ground. That would make the new strong canes the new crown (in time, as the plant grows :-)).