who setup the modem and router the first time?
If the first network ran without a cross over cable, the new one will too 
you are correct, modem direct to system MUST work first.
use a commant prompt and flush the cache
netsh interface ip delete arpcache
then release and renew the DHCP
ipconfig /release Loc*
wait 30 sec
ipconfig /renew
ipconfig /all should now give you something like (partial results shown)
IP Address. . . . . . . . . . . . : 192.168.0.4
Subnet Mask . . . . . . . . . . . : 255.255.255.0
Default Gateway . . . . . . . . . : 192.168.0.1
DHCP Server . . . . . . . . . . . : 192.168.0.1
DNS Servers . . . . . . . . . . . : 24.48.217.227
24.48.217.226
all IP addresses will be dependent upon your ISP and clearly NOT 192.168.*,
but all four above are needed
you should be able to ping the IP address shown (this is yourself 
as well as the gateway address. If so, then your browser should also be
able to access at least your ISP page.
get this working and then solve the Linksys install issues.
I recall the Linksys default login is admin/admin or admin with a blank passwork -- look it up -- and reset the device or return it if you can't login to it. The router doesn't need the modem for you to do this. you can config the router and your system to use it. It will give you back the 192.168.* ip addresses BUT no DNS address until the modem is connected.