Don't any of the 3 preset codes for your Sharp TV work? If you have the original remote you can learn everything and eliminate the code search or missing function problem. Does your TV use the same button for power on and off? Also, try using another button, like channel up or down (with the TV on, of course) when doing the search, and see if this works better.

For your receiver, you may need to change the command mode on the receiver and remote. Click here to learn how to change your Sony receiver (and its remote) to AV1 (or AV2) Command Mode

If this helps, you will still have to learn some functions because not all functions are included in the preset code.

I don't understand the part about not being able to learn them. When you put the 2100 in learn mode, the buttons available for learning should flash, and then when you press the button you want to use to learn the code from from the other remote, it will become solid until the command is learned. If it does not flash, it means you have learned a command on that button, and you will need to delete the learned command before you can learn another one.

I hope I have gotten you started on a solution for your problems, but if you still have questions, let us know.