Before you assume the sites are hacked what you are describing actually sounds like some sort of technical problem and not a hack – “The Dashboard and most functions show a white screen, but I can access BPS functions.”
Scan the sites with the Sucuri SiteCheck scanner, which usually finds most hackers code.
What is a bit worrisome and may indicate that your computer Browser has been hijacked/hacked is that you are unable to be redirected when logging into the Secure Download Area. The Secure Download Area has protection against Browser hijacks/hacks. If your Browser is hijacked/hacked then the redirect will be intentionally stopped/prevented since this could potentially compromise the Secure Download Area.
Download and Install Trend Micro HijackThis on your computer and run it.
http://download.cnet.com/Trend-Micro-HijackThis/3000-8022_4-10227353.html
Download and Install Malwarebytes on your computer and run it.
https://www.malwarebytes.org/downloads/