on the S10 Remote Controller, how do I see the TV input?

Are you asking how to bring up your tv's input select menu?  If so press the tv button at the top and then press the tv/video button below the aux button.  If it works at all (not all tv may support this) your tv's input menu will be displayed and you can use the arrow buttons to navigate it.  On some tv's leaving the tv accepts the selection after a couple of seconds and clears the menu.  Otherwise maybe OK will clear the menu and accept the selection. 

Be sure to push the AT&T button when you are done.

If you are asking something else all I can think of is you should push that AT&T button to allow the remote to control the volume and on/off on both the receiver and the tv.  The remote remembers you pushed the AT&T button so you don't have to do it every time.

The TV I'm using this remote on is a SHARP HD model. I have two other TVs, both SHARPS,

You say the TV Input button on the S20 works on those other two TVs.  Is that SHARP HD model where the S10 doesn't work the same model as those other two?  If so have you tried the S20 on that SHARP HD where the S10 doesn't work?  Does it work there?  If they are the same models then I would expect the S20 to not work on the problem tv either. 

The procedure I summarized for the S10 is correct assuming the remote is programmed with the proper remote code for that tv model.   It works for me on my Sony, not that I ever use it.  As tech support suggested, you should keep the tv remote nearby to do most of the functions the ATT remotes can't do.  All that's really guaranteed for the ATT remotes is on/on and volume.  Switch input can be problematic and anything else is just luck.

If the S20 works on that tv then the S10 should work also.  All I can conclude are three possibilities: (a) you configured it with the wrong program code - close enough to do some of the functions but not all, (b) you didn't follow the exact instructions I listed on the key sequence - press tv, let go, press tv/video, or (c) the remote is indeed defective.

At any rate getting a replacement remote is trivial enough and it will be consistent with your other two so be happy with your new S20.

Your best bet is to use your TV remote.  There will be an 'input' on that one.

The S10 works fine, however it does not have a "TV Input" button on it.

I never thought this was so complicated.  To quote my first post's instructions "press the tv/video button below the aux button", bold emphasis mine here.  Maybe I should have posted a picture.

 [Only look at the annotated red arrow lines.  Ignore the other red lines.  I ripped that picture off the S10 user manual which was pointing to some of the other buttons with red lines.]

It isn't that it's difficult. You don't need to talk down to people. For the S10 some tvs are not compatible. Your wonderful diagram does nothing on mine. For the input to work I must hit the Info button however no button on the crap remote selects one. For some tvs you must use the remote that came with the TV. I can use every other function except input. 

@Bebu1977 

It's not my problem you only read what you want and not the entire thread.  I said in back in post 2:

If it works at all (not all tv may support this) your tv's input menu will be displayed and you can use the arrow buttons to navigate it.

IMO with the S10's input select control it's always going to be easier to use your tv's own remote even when the uverse remote is compatible.  For me the input select on my S10 does work but I never use it because I always keep my tv's remote nearby and grab it instead.