How do I play the piano in the Steam version of FFVII?

First of all, this is the wrong piano to be playing that tune. Only Tifa's piano will give rewards for playing that song, not the mansion piano.

Secondly, yes, getting that noise on the mansion piano is normal. It actually serves as a hint. When you reach this point in the game (not in the flashback) you may find in the mansion a note that says to look:

Behind the Ivory's short of tea and ray

The grammar makes me cringe, but indeed, this piano is short ti and re. And if you look behind this piano, you will find a certain piece of information.

You'll want to play the piano three times. the second and third time will grant you some great item in doing so. During the flashback you get 1 gil from doing it but you need to do it then to get the other items later.

The song you play does haves one note that sounds like it's odd but just finish the song (if you know it). Check out this question I asked in which someone showed a great image of keyboard controls. Since you aren't asking what the notes are for the song I won't tell you here for spoiler reasons.

Also check out this page and this page for more info and help about controls.