The source code provided is just for some of the components of the Kindle firmware. They need to release that to meet the terms of the license to use that software. It is far from complete and of no use to you.
On the
Kindle DX Software Updates web page there are links to download Software Update 2.5.8 and the Kindle Services Update. There are different sets of these files for different DX models. Check your serial number to see which apply to your device.
Since you already have 2.5.8 installed I doubt that the kindle will allow it to be re-installed.
You haven't mentioned the Kindle Services Update. Have you ever installed it?
It was required to be installed to prevent the sort of connectivity problem that you are experiencing. Though you should have had a problem long before now without it. I suggest that you try downloading and installing that update.
Again, you have to use the one for your exact model. There are multiple links on the page that say "Kindle Services Update" and they link to different files.