If it helps at all, you cannot completely turn off Kaspersky, Bitdefender, & probably several other brands of security software. That's a good thing -- if you could turn it off, so could mal-ware, which often does in fact try to disable security software. They use a Service that auto-starts with Windows that cannot be stopped, set to manual, or disabled -- Unless you boot into Safe Mode, which only uses the minimum drivers, services etc.
"This had never happened before with any giveaways in years of successfull installations..."
In another thread a while back Chris was trying to help with similar problems on a few PCs/laptops. I installed fresh copies of Kaspersky in 2 win7 VMs, one 32 bit, one 64 -- neither had ever seen Kaspersky software before. The very same GOTD offers that were being blocked on these machines worked fine in both VMs. That & other evidence suggests that *in some cases*, the complete installed Kaspersky software, or maybe even something that it changes in Windows, does not match a new, fresh install, & that those changes are responsible for the problems installing GOTD offers.
RE: narrowing it further...
Personally, the only way I know of to find all changes would be to do a snapshot of all files/ folders, & registry entries, try to remove everything Kaspersky, verify that GOTD worked, take another snapshot, add Kaspersky, verify GOTD worked, take a 3rd snapshot, then compare the 3. If the 1st verify failed, I'd have to look further for something I missed, & failing that, compare the 2nd snapshot with the same version of Windows on some other hardware that worked with GOTD. If the 2nd verify failed, I'd have to do the same thing, but after adding Kaspersky to the 2nd machine & making sure GOTD worked.
As my VMs worked after adding Kaspersky, & since those were the only Windows installs I had running Kaspersky, I could go no further. [It was probably the only time I've ever felt badly because my VMs & PCs worked properly.]
"So I have to reboot in safe mode with network! What a lot of hassle for a simple program... anyway, will try reboots/exceptions etc. if I can find the time to do that before the availability time runs out!"
Again, personally speaking, a re-boot into Safe Mode isn't all that bad, taking me just a minute or two. The easiest way is probably using msconfig [I type it into the Start Menu run box], but as this PC can boot into a few different copies of Windows, I usually just select the version I want to run on the Windows Boot Menu, & press F8.