How do I remove the paper cover on the analog board in order to access the solder joints? It seems to be held on by adhesive foam pieces.

Click to expand...

It's just double sided foam tape. Gently tear it off, usually it will split the foam and you can glue it back together with a dab of superglue. Alternately you can scrape off the remnants and use new foam tape, 3M makes the stuff, you can buy rolls of it in any decent hardware store or home center.