"Paper Jam Inside" but no paper there

My 5470DW Brother laser printer persists in thinking that there is a paper jam inside. I’ve tried everything that has been suggested, but nothing works. I just tried wiping the very small gray rollers and noticed that the corner of one of the stiff plastic sheets that partly cover the rollers bends up a little. Could that be the problem? And if it is the problem, is there anything I can do to fix it? I thought of warming the plastic a bit, bending it smoothly over the roller (it’s really not bending up much) and holding it there until it cooled off, but I’m afraid to do anything that might make things worse. Any ideas?