The thought of burning and then transferring everything, though, is rather daunting. I have a flash drive, but I have dozens of photo files, some of which are 2 gigs or better.
If I were doing it without DVDs, I would probably just attach the old drive to an existing computer, then make a direct cable connection from the new laptop to the existing computer and copy the files. I always use a crossover ethernet cable for this sort of thing.