OTA does not require a fast internet connection. This is nonsense. It's designed to work even using GPRS, which is why the download size is significantly smaller.
NSU will be of no help because V30 is
only available by FOTA.
There are many potential reasons why a FOTA update could fail, the most likely of which being a problem with the method you're using to connect the phone to the intrernet. If you're using packet data then try over a WLAN - or vice-versa.
Second on the list I'd suggest that there's not enough free memory on your phone's C: drive to store the patches and have enough room to work in. Uninstall a few applications and/or themes and get rid of some messages to free up space on C:.
If none of these work then your best bet is to take the phone into a Nokia Care Point and ask them to do the update. They have methods at their disposal that we members of the general public don't.
As mentioned by post007, always back up your sensitive data before a firmware update. The 5800 has User Data Preservation and you should therefore not lose any data, but better to be safe than sorry.
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