but you won't be able to write posts on the new system. OR copy across the DB and point the old server database config at the new server - this assumes the forum and other software would deal correctly with being 'multiheaded' and not get its session knickers in a twist
Basically moving a whole single box system to a new box will usually incur some down time somewhere, you haven't got enough kit to stage it.
This only occurs if you don't know what you are doing. You can write to a MySQL slave, but you must ensure that once you start writing to it, you don't write to the master. This scenario works perfect for an instant switch-over.
1) Slave MySQL database to the old server
2) Configure a reverse proxy to forward HTTP/HTTPs traffic to the new server
3) [optional] use socat or iptables to forward traffic for POP3/IMAP/SMTP, etc. to the new server also
4) De-configure MySQL slave
5) Update DNS, wait for propagation to occur
6) Decommission old server.
Zero down time and zero data loss.
The reverse proxy should be used, as it will then add the X-Forwarded-For header to the connections, which the new server should be configured using
mod_rpaf (if Apache is used on the new server, Nginx would be better, but that's another topic) to look for and use as the real IP connecting. Just forwarding the data without this will cause the logs to fill with connections that look like they are coming from the old server and any protection on user account login (such as the forum user login) may trigger lockouts due to all the users seeming to come from the same IP address.
Well the SMF not being to connect to database error just occurred again. So it was definitely not a hardware issue.
This is caused by MySQL running out of connections, just increase the max connections if the server is capable of handling it.