Description of the problem
Although you may be able to log on to it locally without a password, Vista, just like XP, does not allow remote access to accounts with a blank password by default.
Description of the solution
The obvious solution is to set a password for the account, another solution is to change the setting below.
Run gpedit.msc
Go to Computer Configuration > Windows Settings > Security Settings > Local Policies > Security Options
Set Accounts: Limit local accounts use of blank passwords to console login only = Disabled
This will change the default Vista behaviour and allow logon over the local network with a blank password.
Additional information:
More information can be found on this link: https://harshasnmp.wordpress.com/2018/03/21/windows-allow-remote-desktop-access-with-blank-passwords/