InDesign and PDF printing boxes instead of shadows - Onscreen looks perfect

I apologize in advance if this has been asked, but I've searched for a few phrases and I'm not sure how else to ask it.

Using InDesign I've created a vector "ribbon" and given it a drop shadow. I've also placed a PSD file with a transparent background on the document.

On screen, the exported PDF and the InDesign screen preview look perfect (View > Overprint Preview is enabled). Here is a screenshot of the exported PDF (v1.5):

When printed on my HP LaserJet 2600n, however, I get these god-awful blocks around the shadow of the ribbon object and the placed PSD file. Here is a photo of the printed page (the camera on my phone washed out the image - it is accurately reproducing the colours):

I've tried converting Spot colours to Process in case the printer was experiencing some issue with the Pantone colours, but the colours are actually printing fine, it seems to be the placed file and the shadow causing issues.

I'd love to learn how to fix this, and more importantly - what causes the issue!