Athlon K75, pci Realtek 8029 (ne2000), fresh 0.4.13 install.
Adapter has an IP address, pinging internet addresses works, but Application Manager consistently cannot download its database. I confirmed that same URL working on a different computer (running Linux) during this testing.
Serial port debug shows this error:
err:(win32ss/user/user32/windows/messagebox.c:1048) MessageBox: L"Unable to download the package! Check Internet Connection!"
Installing realtek's windows 2003 driver was enough for the issue to cease, confirming this is an issue with the ne2000 driver bundled with ReactOS.