I administer Moodle for my high school courses; I'm fairly new to it, so bear with me. I upgraded to 2.6 two days ago and have just started getting the above error instead of my "admin/index.php" page. It seems to only effect site administration; I can still edit courses normally. I also get the same error when I go to "admin/plugins.php" although I can manage plugins by selecting the individual types (blocks, etc.)
This issue can be caused because of an obsolete plugin. As you told that you've updated your moodle version, it is possible that one (or more) of your plugins(apart from the default one) might not be supporting this moodle latest version.
Its just a guess.
Apart from this, did you enabled debugging and tried to find what might be causing the problems???
If "Display debug messages debugdisplay" is ticked then you'll be able to see error messages on same html page, else you've to see server logs to see what is the error.
The description is there "Set to on, the error reporting will go to the HTML page. This is practical, but breaks XHTML, JS, cookies and HTTP headers in general. Set to off, it will send the output to your server logs, allowing better debugging. The PHP setting error_log controls which log this goes to."
I think I fixed it; I had to turn on the developer debugging mode, which showed a problem with the Essential theme, which I thought I had uninstalled. I reinstalled the theme and now it seems to work.
I still have a lot of plugins that I have to uninstall, hopefully it won't break again.