Could you go to your command prompt (windows key and r, then type cmd) and type ipconfig /all please. Then look for what it says for your dns. If you are getting dns issues, we can advise new dns servers to use, as you don't seem to have advised as to whether swapping dns servers to Google worked, as Keith suggested earlier.
When you get the connection/dns page come up, is the laptop still showing as connected wirelessly? I used to use a vista laptop that would display the same sort of pages, but it was because the laptop had dropped the wireless connection, even though devices further away had kept theirs. The laptop later got reformatted to a decent OS:)
Next time you get one of the dns/connection pages, may be worth bringing up the command prompt again and just trying to ping the router (command is ping followed by the gateway address of your router, likely to be 192.168.1.254 if you haven't changed it, but it will show on then ipconfig command I requested earlier and will show as default gateway). If you get timeouts on the pings, or very high results, that would indicate what is happening, but not necessarily why.
EDIT: Could also try ipconfig /flushdns when on the command prompt, just in case we are looking at a dns issue.
Can you connect and use the Internet OK when connected by Ethernet. If you can then there would be appear to be a fault only with the wireless side of things.When you fitted the new screen are you sure you connected it up correctly. It may be that the aerial for the wireless card runs around the screen and the connection is making and breaking which would give you very poor performance.
Without using something like Wireshark, to analyse the data being passed by the laptop, its difficult to see what else you could try, apart from using a different router.
Wireshark would require you to use an Ethernet connection, as most wireless cards do not support promiscuous monitoring.
There maybe something odd about the DNS requests, which the home hub does not like.
Have you checked that the wireless drivers are up to date, using the Samsung website?
You could also try changing the wireless encryption to WPA only.