Maybe your system isn't able to give your media player enough resources when the other program loads.

Does it only happen when certain programs load or when any program loads?

Something you can try is pressing "Ctrl+Alt+Del", selecting the "Processes" tab, right-clicking the process that is playing the music (wmplayer.exe for Windows Media Player), select "Set Priority", and changing the priority to "Above Normal" or "High". This will tell the system to give preferential treatment to the program playing your music so that it will have a better chance to get access to the resources it needs. This can sometimes cause the problem to lock up or make the program "freak out", but it will be a good way to try to see if it addresses your problem.

It may be that you have too much junkware/malware on your system that is eating up too many resources. My system only lags with video playback while doing processor or memory intensive tasks, never audio. It's also possible that you are just trying to run too much. A system is only capable of giving a certain level of performance.