Okay, either I have an inability to operate simple electronics devices (unlikely), cannot read instructions properly (probable), or Sony screwed up (more probable). Here is the issue, and I hope I can explain this well enough:

1- my parents and I bought my girlfriend a DVD player for Christmas. this one: the Sony DVP-NS315B

2- the remote that comes with it has a TV power button (this is to make sure I'm not crazy later in the post)

3- I look through the manual on how to train the remote to operate the TV. I find two columns on the subject (totaling one page). In it, they show pictures of two remotes. Fine, I've seen manuals that apply to different models before, no big deal. I am holding the remote pictured on the left. There are no remote-specific instructions.

4- the instructions for training the remote are not unusual. Hold the TV power button down while dialing in the code for the make of the TV, provided in a table of manufacturers in the manual. That's fine. My girlfriend's TV is a Sharp. The code for Sharp is 18. What's the problem?

The remote has no numbers on it.

This is where I am either going totally nuts, or the manual is grossly incomplete. There is a picture of the remote I am holding in the manual, pictured with no numbers. What's worse is that there are little arrows pointing at the other remote to where the numbers are on that one! AH!

I looked over the sparse instructions, and there is no mention of this amazing occurance. The instructions are very simple. Hold the power button, press 18, release the power button.

What am I doing wrong?

Looking at the specs on that page you linked to I noticed that the remote specification says:
Multibrand Remote: No

So the likelihood of it controlling a Non-sony TV is about 0.
I have lots of Sony Remotes with TV buttons on them and they only control Sony TVs.

I gather its a bit different in the US where the TV buttons usually control the other brands of TV, but perhaps in this case this model of DVD player only "does" Sony TVs?

[or it could be that the buttons on it can be used lilke a numeric keypad of sorts, but presumably you'd need a chart to see what button is what number].

You could of course try holding the TV power button and then some other buttons to see if that "takes" and if the IR led flashes differently when you press the TV button. But you could just call Sony and ask them to confirm.

That's what I thought as well, but there is a picture of the remote in the instructions. If that is the case, there should certainly be a note in the manual that says "model 315 remote only controls Sony TV's" or something like that. I also tried pressing what would be one and eight on the remote, but that didn't work and I felt silly for even doing it

Okay going off topic why oh why do some remote controls have an eject button. if you want to eject the video/cd/dvd there is a good chance you will be standing next to the machine

rant over

Saves time! you have the remote in hand when in chair. Press eject button and tray opens just in time for you getting up to reach the tray. Its great! Don't tell me you've never used it!

I use it to freak out my son... He thinks I'm magic. Of course he's 15 mo. old.

I don't know, but I did manage to spill a glass of red wine on the floor from 30 paces using one once. Which wasn't quite what I meant to do...

In reply to:

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I don't know, but I did manage to spill a glass of red wine on the floor from 30 paces using one once. Which wasn't quite what I meant to do...

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Reminds me of an old TV advert for a bank