Possible solution:
run 'mysqld' (or any of it's flavors), then connect to the server with the command:
mysql -h 'IPaddress', so e.g
mysql -h 172.21.32.150
This works for me !
Somehow your machine may be confused about the 'localhost', and this command then gets around this.
I had the same problem myself and I still do not understand why it happens. There is a hint to this on page 86 or so of the mysql maual, where it is suggested that the hosts file may not contain the '127.0.0.1 localhost' entry.
In my case there seems to be nothing wrong with the hosts file (win98: hosts and lmhosts file both contain the 127.0.0.1 localhost entry, and I have no firewall runnning on the fialing machine; I do on the other desktop) and it still comes up with '2003' if I do a simple 'mysql' or even a 'mysql -h localhost'.
My own story ? I have a couple of machines in a lcoal network: two desktops and a laptop. exactly the same installation procedure on al three machines resulted in two machines working perfectly fine, and one of them failing with the '2003' error. I first thought it could have something to do with the amount of memory, because the failing machine only had 48 MB, but the solution mentioned above cleared it completely.
I then spent time reading through hundreds of pages vagely or clearly referring to this error, and none of the solutions posted by people in reply worked for me. Then I got down into the manual again and found the reference on page 86. That got me to play with the options on 'mysql' and that finally brought me the solution.
So let us know in this forum whether the psoted solution worked for you. It may help other people to know !
Cheers
John