You can check in your registry and see if the key shows the same as the picture in this post:
10240 to 10525 - No Upgrade Offered, no errors.
If so, your machine is ready. If Windows Update does not start downloading 10525 now, try a few reboots.
(Otherwise, we have a little trick to try and force it, which we can try later.)
When it does start downloading, remember to refresh the folder $Windows.~BT\Sources and grab the install.esd files as soon as Windows is 100% download, but before installing (do it immediately when it starts "preparing to install"). You can even disconnect from the internet once the download is 100%, to prevent the installation from taking the esd file away.