Was dragged out of bed by swmbo last night with this issue as she was updating the bank details at an ungodly hour.
It appears, at least in my case, with Windows 8, that the latest update of that piece of ****e OS, seems to have removed Java. I reinstalled the latest version of Java (which it though was a new install, hence my conclusion that the recent windows updates had removed it). That worked for me, Danske is now working again on both windows (desktop IE), and chrome.
And it wasn't the banks issue, it was a Windows problem,
Apologies for the tone - but I get that way after upgrading to windows 8, and having to fix its snafu's in the early hours of the morning.