Test with the Laptop
First I would hook up your laptop to the Ethernet in the second building and see if you get an ip address from the first router. If not there could be a cable issue or a bad port on the First router, so try another port. How do you have the 2nd router set? you said bridge mode but is it still handing out an ip address? If it is then turn dhcp off What port on the second router do you have the cable ran into? hopefully its in port 1,2,3 or 4. it wont work in WAN port.
You can set the 2nd router to a static like the previous user said and It would be easier to be managed. For example if your main router hands out an Ip address in the range of 192.168.1.1 to 192.168.1.50 give the second router a 192.168.1.2 and set that ip address in the main router dhcp reservation.
Oh and one more question how many devices will connect to the internet? If its more than 50 then you need to change the amount of ip address the first router hands out to the clients, If its over 100 clients then you might have to change the subnet.
Hope this helps
Michael
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