So my brother has got interested in Minecraft, but isn't convinced to buy it yet - we want to try setting up a local network to play with each other. (So, he'll be either using my login or in offline mode for now.)

I've got Win 7 Ultimate and he's got Win 7 Starter (ASUS Netbook).

Each of us can run an MC server on our own machine and connect locally to that. (Obviously his machine is too low spec to properly run the server, so it needs to work with my machine running the server.)

His machine can succesfully ping/tracert my machine (by ip or name) so the machines are talking at a basic level.

I've told Windows Firewall on both machines to accept incoming and outgoing for the relevant port.

Still can't get Minecraft to connect to my server from his machine - just gives a generic timeout / can't connect message in MC.

Am I missing something obvious?

Disable the firewall on each machine. If it works then you know the issue straight away. If not, keep guessing!

Oh sorry, forgot to say I did that earlier and it didn't help.

Thinking maybe it's a port thing with the router? What's the easiest way to rule that out?

Our phones (one Android, one iPhone 3G) were able to connect to each other with the mobile edition (free demo; not giving Notch £5 for it!), over the same wifi network.

Got it working with Hamachi.

Of course, since we've only got my account, only one of us can be logged in at one time .... until I put the server in offline mode, and my brother plays offline, and now it looks like we can both play together.

Yay Hamachi. :)

your problems (without Hamachi) most likely stem from the way minecraft authenticates accounts, you and your brother will both have the same external IP - I believe the official MC server software will only allow one connection per IP address

That causes a "bad login" error, not a timeout?

could be, for me the errors seem to be randomly generated, get different ones all the time on Ant's server