In addition to the points already raised above, modern use of the English language is somewhat abrupt.
Modern authors tend to go straight for the punch. For example, King (who I love by the way) opens The Stand, after the intial dialogue, thus:
First she glanced at the clock on the night table and saw it was quarter past two in the morning. Charlie shouldn't even be here; he should be on shift. Then she got her first good look at him and something leaped up insde her, some deadly intuition.
Immediately there is a sense of suspense and drama. But the language is basic. Look again at A Tale of Two Cities:
It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way -
The text here is busy, and elaborate, but it is beautiful. The English language used to the most advanced of its time. We talk of language progressing, evolving, but I think it is the opposite when you apply the theory to fictional writing. We've gone from Dickens using English in this way, to King using the very basics to form his initial first few lines. Both are skilled writers, and are justly famed and reknowned for it.
Classical writing uses the text to draw in the reader, but the modern writer doesn't have the need for this. The human race has advanced tremendously since Dickens. Technology, religion, the way we percieve relationships. Dickens could never have begun a novel by having a man wake up his female counterpart. It would have been beyond controversial.
Additionally, during the time when Dickens was writing, education would have been extremely basic for the poor. Only the richer would be educated enough to grasp his language, and only the richer would have the money for books in the first place. It was a matter of practicality.
Dickens was limited in his target audience, where as King is far less limited. That doesn't make King any less of a writer of course.
Rather than look upon classics as a chore, try to view it more as a privilege. You're getting to read something that even at its time of publication most wouldn't have been able to read, by reading the classics you're on a journey to discovery. There will be some you like, some you don't, some you love, and some you don't. But each and every book, whether modern or classic, is both an achievement and a privilege, for the writer, and for the reader.