The original wallet was on my desktop, but I didn't have enough space for all of the blocks. So I had to start one on my laptop. Could I just move the one from my desktop to my laptop?
Yes, you should be able to. Press Win+R to bring up the run menu, type in
%appdata% and press enter. Go into the
Bitcoin directory, and copy the
wallet.dat file into the same directory on your laptop. Replace the file on your laptop, as long as you haven't sent any coins to the wallet on your laptop. If you have, make sure to make a backup of it first.