Hmm ... I had similar problems with two Vista Laptops. In my case they would sometimes connect, frequently would connect with local network only, and sometimes internet would be fine. Research on the internet suggested that this was not an uncommon problem ... but that there were no common solutions. In the end I went with ensuring all driver and windows software was fully up to date, then updating the firmware in my router. I wish I could say that fixed it ... but unfortunately Windows recognised the firmware download as being from an internet source and locked it. Therefore when I tried to apply the new firmware to the router I could not access it ... and urm that left the router without firmware.
My fix was then to buy a brand new modem/router .... and that worked.