OK - using your 2nd computer which hopefully has an ethernet skt for the yellow cable, connect to the router. With a second yellow - ethernet cable - connect as you have done to the modem.
On 2nd computer open a web page and type in the address of the router 192.168.?.?- the actual address may be printed on the router or in the manual - follow the setup wizard and establish a connection to the internet.
Then disconnect the 2nd computer and then install the wireless adapter.