To write a music player with delphi, you can consider using the BASS Music Library. Bass Audio Library is a free audio processing class library for non-commercial users, which has powerful functions and supports almost all audio decoding and coding.
The official home page of BASS provides sample codes of various languages and platforms, including C, delphi, VB, etc. Among them, the delphi language sample includes BaseTest, which shows simple music playback:
Directory of sample files:
Running effect of the code:
The code can be downloaded from the attachment or directly to official website of Bass.