I could solve my problem, but am not sure which task did the job, as I changed two things at a a time.
I decided to do a complete reinstall of my BE2010 application and all related products such as remote agents. In order to do this, I double checked my licences online and found out that not all had been upgraded to BE Exec 13 (i.e. 2010), so iwent through the whole upgrade process.
After that I uninstalled all remote agents and finally removed the application itself from the media server. A couple of reboots later I reinstalled BE 2010 and downloaded and installed Hotfix 348284. Then I deployed all remote agents. I still couldn't do a push install to my domain controller, though.
I had all my jobs and lists saved, and ran a Backup of foresaid fileserver. All went well. Last night's backup was fine, too. I'm back on track!
Yours,
Frank