1) I'd stay away from Belkin stuff in general. They seem to have a reputation for being good, but from my experience they're awful.
2) You could try a MIMO antenna type (multi in, multi out) router, with 802.11n wireless. (This is pre-n as the above poster says; it's not technically final yet.)
That should help.
But several walls may be too much for that even, to get at least a decent strength. If so, and you really want to go wireless, you can get a wireless range extender for about �40 or so, and simply put that on the inside wall of your house nearest the shed. It should pick up the router's signal and simply amplify it to the shed.
But really, pug's suggestion of an ethernet cable is the guaranteed one. But I'm not sure if they're rated for outdoor usage, but I think they should be fine.
(Also, buying from amazon.co.uk or ebuyer.com will likely be a lot cheaper.)