Using memory causes music/videos to stop playing

I'm having a problem with music/videos refusing to start playing. More specifically, it appears that this problem only occurs when I'm using a memory-intensive program.

Some things I'll be doing when music will not play is playing games (League of Legends mostly), talking in a Steam or Skype call, etc.

YouTube, Spotify, iTunes etc. all refuse to play music. The play button works but the media will stay at 0 seconds.

I'm using a Dell Inspiron N5110 with 4 GB RAM, I would have thought this would be enough to run multiple processes (ie. playing music while playing games) at the same time.