Have you made sure you have properly closed the application? How about trying a factory reset of the device, maybe it is glitching due to something lingering from the install of that other music player?
When the song is playing, does the music app show up...can you see what app is actually playing the song? Is it possible you have set the song as a notification for something like a facebook, email, next SMS alert...or as an alarm clock for that matter?
I'd agree with cryptiq - it must be some type of notification or alarm. If it's happening at the same time, I'd look at the alarm. If it's seemingly random times, I'd look at your notifications. And if you have young children who sometimes play with their own apps on your phone or may have gotten hold of it, then it could be anything. Just keep your media volume muted in the meantime until you get it figured out.
You also may want to try temporarily removing the song from the SD card. Perhaps whatever is accessing the song will throw an error the next time it tries to play it and it may give you a clue as to what's causing the problem.
Need to be sure it is 100% random.
Example - could it have been time for a notification from an app?
Does said app use a file from the SD card for it's notification sound?
Has SDcard been unmounted or cycled or scanned by any app since the last time you got a notification from our example app?
What I'm getting at -
It's a known issue that if you move enough data around on your SDcard the locations of the files change enough so that you need to reset app notifications. Let's be honest, Android still has some weird issues and this is one of them.
What if this is similar and it just appears random because it's so far fetched?