Alright, I see what you mean, but that doesn't mean that the key is indiscernible. The song is in Bb minor. That's the key. Bb's the root and the quality of the key is minor.
The second chord in the progression however is ostensibly not in the key because the minor 6th (Gb) is augmented to a major 6th (G natural) to match what's happening in the melody. That's okay. It doesn't screw up the key at all, the progression is just adjusting harmonically to fit the accidental in the melody.
The G moves down to Eb in the melody, which gives us a pretty strong interval to work off of, and since the background line (what you're calling the arpeggio) leans pretty strongly on Bb at the bottom (Bb G Ab G Bb G Ab G), we get three notes that fit pretty well together: Eb G and Bb, aka an Eb major chord.
Try using Eb major (i.e. major 4th chord) as the second chord in your progression. The rest of the progression should fit nicely into Bb minor.