0110 is the device code to assign to AUX device key:
1. Press AUX
2. Press and hold SETUP until AUX light blinks twice
3. Type 0110
Now try POWER to power on (power off won't work yet)
Also if you haven't change the volume lock yet you need to unlock it for AUX:
1. Press AUX
2. Press and hold SETUP until AUX blinks twice
3. Type 993 (AUX blinks twice)
4. Press VOL- (AUX blinks four times)
Now you should be able to control the volume of the receiver
If those work, I can show you how to program other keys. For example, to get POWER OFF on SHIFT-POWER ("shift" is press and release SETUP and then POWER):
1. Press AUX
2. Press and hold SETUP (AUX blinks twice)
3. Type 994
4. Press (not hold) SETUP
5. Type 00002
6. Press (not hold) SETUP
7. Press POWER
Now you should have Power off by pressing and releasing SETUP and then press POWER (if you don't like the shift function, you can always assign it to some other key and leave out step 6).
If all the above work, that probably means your HK receiver is using the standard HK remote protocol. You will be able to get some commands to work, like most of the INPUT keys, but you won't be able to get some keys to work, like DTS, Dolby, Prescan up and down, arrow keys, and some others. I'll give you the other commands to program if you can get the above to work.
If you do need other keys that are not possible by default, there is a way to upload an upgrade via cable connected to a computer to the remote to have the correct protocol. The Cox remote is a "JP1.1" remote and it would involve buying or making a cable and using a couple of free programs on the computer to program and upgrade the remote. You can read about it
here and
here. I can help you through the steps if you are interested.