I take it you are now in UK and have taken the router with you back to UK?
1. The black screen on laptop, have you tried static discharge? - with the laptop powered off, remove the battery and mains cable, press and hold the power on button for at least 60 seconds. replace the power chord (not the battery) and power on, see if that works.
2. You say you are getting a list of connections for wifi, on Ipad, which obviously has the wifi connection on, so I expect you are getting a list of those who have wifi in your area, next to them it should say - -name of connection- and if it is secured (may have a little padlock icon) and to connect you need their password to connect.
3. In that list is your router showing? if it has not been given a name then it should be the make of the router - TPlink - belkin or whatever, if you had a password for that where it was installed before, that password will be the one it wants.
As for resetting the router, there is a reset button on the back of the router and you can press that but it will wipe all previous setup info and you will have to reset up the settings
hope that is some sort of help?