Looks like using batch file with:
net use \\server\D /user:trodas xxx
...do the trick, but what I can use in case the machine has just empty pass? I tried:
net use \\duron\D /user:ivanka
...but it just asked me to specify a pass...

Any help with this one, or perhaps an explaination why I seems to remember these logins was saved in SP3?
Other than that, the batch file is kinda easy. I just added it up into the "Run at start" Startup menu folder and with details set in the icon to run as minimized and as workaround it seems to be pretty easy to do and working well

But I seems to remember that my Win2k SP3 remembered passwords to other computers - oh, wait, we might used just logins with empty passwords at the time?
But clearly ti remember that - maybe I used account trodas and same trodas accounts are on network drivers? Nah, my bro and sis machines has not trodas logins, or perhaps we create them?

I don't remember now.