As i understand, the wireless signal is excellent in the lap top. but you are able to access the internet for a while.
my suggestion is assign the static ip address,subnet mask and default gateway in router range.
also assign static DNS in the laptop.
preferred DNS is 188.8.131.52
alternate DNS is 184.108.40.206
the steps to assign static ip address and Static DNS in the lap top.
--click on start .
--go to control panel.
--double click on network connections.
--right click on "wirelelss network connection".
--go to properties.
--you could find a small white box with list of options with check marks in front.
--In the high light internet protocol TCP/IP and click on properties button.
--there u could find 2 options, in that select use this ip addrress.
--in that area enter the ip address,subnet mask and default gatewat.
--in the bottom of the same screen u can find 2 options.
--select use this DNS address and enter the DNS i have given and say ok.
--and say close in propertis screen.
--restart the lap top.
hope this will help u.:-)