thirdly the ssid of each router should be different to prevent possible issues however im not sure if an ssid conflict can happen but at least you can tell what router your connected too. and finally as mentioned earlier in this thread, check mac filtering in the routers config (both of them) and make sure your machine is either added to the list or make sure mac filtering is off (not recommended). im not gonna get into wps but it could also help but i doubt the lappy supports it, at least in hardware. i think i covered everything good luck and post success or failure.
*edit* if you cant get access to the router interface for whatever reason you must use a cable connection.
i can see several problems. firstly are both routers set to be dhcp hosts? if so change one of them then reboot both. second unless your file sharing (torrents, website hosting or ftp etc.) you should use automatic ip config - it saves a lot of the hassle, so if possible set both machines to auto or make them both manual and assign them different ip addresses on the same subnet (e.g. 192.168.0.x where x is the address from 2 - 254) and also make sure the routers are both on the same subnet so if one is 192.168.0.1 then best bet is to make the second 192.168.0.100 - always good practice to keep them well apart, they dont have to be it is just easier.