Here's what I did originally: I flashed clockworkmod (via Odin) and booted into recovery. I then installed the cyanogenmod zip file that I had copied onto the sdcard.
When it failed to boot, I tried several things: I flashed TWRP (via Odin) and then did a factory reset and system wipe, installed cyanogenmod (from TWRP) and did the factory reset again. Same problem, the system will get stuck in the boot loop. I also tried an earlier version of cyanogenmod, same problem.
I am quite sure that I downloaded all the right files for my device. I searched online and saw other people who had that problem, and solved it by wiping the cache/data after the install. This didn't work for me.
I don't know what else to try, so please reply if you have any ideas!