[Found: Music Dream I] Music player with Batman
 

Not technically a game if I remember correctly but since Batman is involved its hard searching for it and get relevant result.

It is a music player where one can select and play songs. It has a picture of Batman as a background image.

It's a so called "music disk", and I think the one you're looking for is Music Dream 1: http://bitworld.bitfellas.org/demo.php?id=7060

Also check out these ones, same sound and style from the same group of people:

Music Dream 2: http://bitworld.bitfellas.org/demo.php?id=7498
Crystal Symphonies: http://bitworld.bitfellas.org/demo.php?id=7764
Crystal Symphonies 2: http://bitworld.bitfellas.org/demo.php?id=8304

Thanks, this seems to be it!

Edit Bonus: Awesome music http://www.youtube.com/watch?v=lDlxWNwcrRU :>