I would setup the new computer with a complete backup copy of the old surgemail directory, which will probably take a whole day or longer.
Then install a fresh install of 6xx on top of it, then turn on and test (using a 2nd live IP address thats different than the old server).
Once functional, then goto Netwinsite and register a 2nd serial number, then contactHIDDEN@ and let them know it will be temporary,
then set old computer as master and new computer as slave and copy any new emails over.
(I don't remember if Mirroring worked well back on version 4.)
Also note that this will NOT copy all settings and all mailboxes.
You should tell the Mirroring feature exactly what to copy over.  NetWin has a separate Help page for that.
After mirroring is complete, just change the serial number and authenticate again.
You can either map the DNS to the new IP address (remember to shorten the TTL to 3 minutes or some short duration first, or you can swap IP addresses.  
Shutdown surgemail (net stop surgemail) Go into surgemail.ini and look for the IP and change accordingly, then change the NIC card IP on both computers, then reboot both, then net start surgemail.  The key here is to have the NIC IP be the same as the Surgemail IP.

BarryZ
Reading PA