my beautiful palm tree

There are a lot of questions asked about cordylines, probably as they have suffered from the bad winter we had. I don't know much about this plant but if you look at the gardening questions page, to the right under "by popular genus", you may get your answer here. Good luck...:o)

If there's no growth at the top starting, you can cut it down by half to see if that forces growth either from the base or up the remaining stem. If nothing by end of June, it's a goner, I'm afraid.