I have my own broadband connection, however as this sometimes goes
down, I would like find out if anyone has an open connection, just for
checking email and basic surfing.

What hardware do I need for a desktop PC to scan for an open connection
and to pick it up?

As it happens I just bought a wireless router off eBay, a Netgear
DG834g, and I will be able leave some of my bandwidth open. Is is
possible to restrict the amount I leave open?

Could I use this router to pick up open internet connections?

any help , links appreciated,

JimBob