You're booting into the download partition, which means that the rest of the firmware in the phone is either so corrupted that it can't boot, or the hardware went (the part of the eMMC storage that the main ROM partition was on). Try reflashing the ROM (see
[Samsung] How to flash Stock ROM via ODIN If you can get to the download screen, you can flash a ROM.) If it works, you have your phone back. If it doesn't, you'll know that you need a new motherboard, which probably wouldn't pay for a Note 2 (There are AT&T, Sprint and unlocked [meaning AT&T or T-Mobile] versions available on swappa.com - the Sprint for $50, the others for about $100.)