To run a memtest, download memtest86+, burn it to a CD, and it should boot up and run.
However, a newly occurring BSOD might be the result of a bad driver (especially if it doesn't manifest under Safe Mode). Did you install any new/updated drivers recently? Is there a restore point you could restore to prior to that? Otherwise, you might need to back-up data and re-install windows, then careful upgrade your drivers (creating restore points) to determine which one caused the issue, then avoid it.
edit: by saying "only a DVD drive", are you saying you can not burn disks? Do you have any friends that can? Can you burn a disk at school or a library or Kinkos or something? You can probably also create a bootable USB drive with memtest on it, Google should be your friend there.