Losing connection to server during query

Lo all,

We have recently just moved the db from a socket connection
on the same machine to a port connection on another machine.
The network is a LAN.

I'm getting this error:

Unable to connect to database:DBI
connect('database=tm;host=mysqldb;port=3307','tm',...) failed: Lost
connection to MySQL server during query

I'm not quite sure why it says during the query as it happens during
my connect subroutine which only issues a connect. Anyway, how
might I stop this happening and what server variables (if any) might
I change.
The server is a SMP with 1gb memory, so I have some room for
manouvre.
Any clue, pointers to rtfm much appreciated.

John