As soon as I posted this I realized I did not have the latest version of jDownloads. I noticed a point release (1.9.1) and as soon as I installed it, the error went away. I'm leaving this post in case it helps someone else.
I saw several threads talking about a blank screen but none of them fit my scenario exactly. I looked at the FAQ and did not see any tips or tricks there that helped me narrow down the issue.
I have a site that had jDownloads working. It is a Joomla 2.5.8 site with the latest version of jDownloads (show in the extensions manager as 1.9.0 Stable build 925). The site was running on PHP 5.2.17 and is hosted.
My hosting provider is moving everyone up to 5.4 (5.4.10 to be exact), so I went ahead and forced the version upgrade. At this point, without any other changes to the system or plugins, the jDownloads pages fail to render at all and there is no discernable error. I was able to flip the site back to PHP 5.2.17 and the pages render again. Something is preventing the pages from rendering that is PHP related but I am at a loss to determine what.
I set the PHP error level at development in the control panel and turned debugging on (and caching off) and, while I got other strict warnings, I did not see any errors. I checked the Apache error logs from the hosting provider and I see the page load but no errors.
In order to try and track this down, I installed WAMP locally and took an Akeeba backup of my site and restored it locally. I had the site up and running and then turned on debugging again (hoping that I would catch some error). I observed the same behavior on a local WAMP server install of my site as on my hosting provider. I even started down the path of setting up Eclipse to debug the code through XDebug but ran into a snag and was not able to get it running.
I am open to suggestions for ways to track this down this error. I'm not opposed to putting in raw debugging statements to narrow things down and I think that's where I'm headed next. I don't seem to have any issues with the administration control panel and I was able to upload new documents in the backend on PHP 5.4.x before I realized there was any sort of problem.
If anyone has any suggestions for where to look, they would be appreciated.