Right, I'm with you. In which case, there's nothing (I think) wrong with the laptop or the connection to said router, it is, as you say, the connection coming in to the router itself. Repair is actually therefore working, in that it's reconnecting the laptop to the router, but obv that won't do any good if it's the router itself that needs restarting. This also explains why you have the same problem when connected via a cable. On the plus side, it sounds like you may have got a nice wireless dongle out of Orange (if you can ever get the software running but we can come back to that).
It might be worth looking at the router's log files. You should be able to log in to the router from the laptop - looking at a random Netgear manual it looks like going to the webpage www.routerlogin.net [I deliberately haven't converted that to a link] should open up the admin screen. The username is admin and the password is always password unless you've changed it. Have you done this with Orange when you've been changing passwords? If not, or you don't fancy it, don't worry - I actually don't know what you'll be able to see as DH always sorts out our router. If you do want to give it a try, let me know what you can see (you can always just exit without saving anything) and then we can always have a look for the manual for your actual router.
The other thing I would do, when it next stops working, is have a look at the lights on the front of the router. Have Orange asked you to do that? There's probably one light for the connection from the router out to the internet, and another for the connection from the router in to your network at home. Would be interesting to know what colours they both are.
By the way, I'm assuming your home wireless network is password protected - just wondered if maybe the connection was getting overloaded by traffic from other people and that's why it was conking out.