What are the procedures for upgrading a ProLiant ML370 G5 firmware REMOTELY? I’m thinking via its iLO, and if so, where do I access to do the upgrade

When you first turn the server on, there's a a section during startup that says "Push F8 to enter iLO Configuration" (might be some other function key). Do that and fill in the network information and setup a login.

Once that's done, open a web browser at your computer and enter the IP you configured. It should be very self explanatory from there.

The iLO configuration is not stored on disk, and not in the BIOS, so there's a decent chance it isn't clear. Also, how your VPN works and how to use it is completely outside the scope of using iLO.

All of HP's example scripts use <RIBCL VERSION="2.0">, but that's the only difference I see. I'm also not sure whether renaming a user in this way will actually work, so maybe that's it. Try just changing the password:

<RIBCL VERSION="2.0">
   <LOGIN USER_LOGIN="Administrator" PASSWORD="does-not-matter">
      <USER_INFO MODE="write">
         <MOD_USER USER_LOGIN="Administrator">
            <PASSWORD value="new-password"/>
         </MOD_USER>
      </USER_INFO>
   </LOGIN>
</RIBCL>

Also be aware that characters <>"& are not supported properly in passwords (iLO's don't quite parse XML correctly).

If that still fails, try using hpilo_cli, which can generate XML for you and pipe it through hponcfg.