Dubrovnik is unfortunately not the best connected place in the world.
I once caught a train from Split to Salzburg via Zagreb, Slovenia and Vienna. I did this using a Eurail regional pass for Slovenia/Croatia/Austria and this turned out to be quite cost effective. I wonder if you could get something similar but incorporating Hungary or Czech Republic?
To get to Split I flew Ryanair to Ancona (cheap) and then caught an overnight ferry from Ancona to Split, which was quite affordable, especially with an ISIC card.