Prior to this, did you attempt to dirty flash (flashing w/o wiping data) any roms to your note 2?

If so, then you probably bricked your device. You can try:

1. Reflash the rom. *Fingers crossed*

2.ONLY IF YOU DON'T MIND WIPING YOUR APP DATA. This means you will lose your apps, and will be prompt to setup Google account again during first boot.
Boot into recovery, wipe cache, dalvik, data.

If no, you can try:

1. Boot into recovery, try wiping cache and dalvik. Reboot.

2. ONLY IF YOU DON'T MIND WIPING YOUR APP DATA. This means you will lose your apps, and will be prompt to setup Google account again during first boot.
Boot into recovery, wipe cache, dalvik, data.
BTW, what is hard reset option? Recovery mode?
If you are in downloading mode instead of Recovery mode, you may have pressed the wrong button combinations.
Try Power+Home+Volumedown instead? (not familiar with samsung devices, sorry)

Your driver won't show if the device is unable to fully boot

You can try manually flashing the recovery again through Odin.

Check out this video maybe:

Install TWRP recovery via Odin

[WARNING] I'm not responsible if you bricked/hard-bricked your phone.

Oh, I forgot you need to boot up in order to use Odin. Haha, my bad.

Another method is via ADB fastboot.

You'll need to:

1. Download and install ADB & fastboot drivers. [Google adb & fastboot tool]
2. Download a latest TWRP of your device. [Google note 2 TWRP]
3. Place your downloaded TWRP.img into the folder that contains the "fastboot" bat file.
4. Boot your device into Bootloader mode. (not sure if download mode and bootloader mode are the same. You need to check on this yourself)
5. Open up "fastboot". Type in the cmd:

"fastboot flash xxxxx.img"    //where xxxx is the file name of your downloaded TWRP.

"adb reboot recovery"  //this should bring you to the recovery mode

More detailed, you can check HERE and scroll to "Procedure".

My nexus 7 bricked the other day. Lost my recovery as well. This is how I resolved it.

After doing all this, you may try those steps as said previously in my other post. If you are still unable to boot, you need to reflash your rom. Look under CynogenMod or XDA to see if there's any rom suitable for you. Use ADB to push the file into your device, and flash via recovery. Alternatively, i think you can "fastboot flash" the rom using fastboot as well.

P/S: Be ready to lose some data. EG: Apps, text, photos, videos, etc.
Also be aware that this is based on my experience as a Nexus 7 user. Not sure if there's any interfering samsung firmware/security.