When I turn on my computer, I can hear the windows’ chime in my headphones that are plugged into the audio out port and...

While running a program, the computer will shut down unexpectedly and is warm to the touch.

Try your headphones in a different computer, that way you can test whether or not it is your headphones that are malfunctioning. If you can, also try and verify the sound file (corrupted files can have distorted audio). If neither of those solve the issue, try to update your audio drivers. If your issue is still not fixed, you may have a damaged audio port or sound card. However, because both of these components are integrated onto the motherboard the entire motherboard will need to be replaced.