the answer is YES
you piggy-back the router onto the fibre modem, you can do this if
a) the fibre modem has a LAN port (which it will have)
b) the fibre modem allows its IP range to be changed
c) the spare router allows DHCP to be disabled
d) the spare router allows its LAN IP Address to be changed
if yes to all 4 then you can do this.
you simply shorten the Fibre Modems LAN Range by 1,
e.g. (assuming your Fibre Modem is on 192.168.0.1) change 192.168.0.2 - 192.168.0.254 to
192.168.0.3 - 192.168.0.254
as the device is on 0.1 and the rest of the range starts from 0.3 to 0.254 , this leaves 0.2 for the 2nd router to use...
(if your fibre modem is on 192.168.1.254 and range is 192.168.1.1 - 192.168.1.253 then follow suit by changing the 192.168.1.1 to 192.168.1.2 and using the 192.168.1.1 for the 2nd router)
now once you done the above in the fibre modem you can turn off any wi-fi in the fibre modem ...assuming it has any.
now unplug the fibre modem and plug in the 2nd router, log in, disable DHCP and set its LAN IP Address (not the range) to the address you free'd up previously... e.g. 192.168.0.2 (or 192.168.1.1) then apply & save - you will now use that IP Address to access this router instead of 192.168.0.1
now with both unplugged and powered down/off, plug in the Fibre Modem and turn it on, give it time to connect to internet, then plug a LAN cable from one of its LAN ports to any of the 2nd routers LAN ports, plug in and turn on the 2nd router and wait for a while - you should now be able to use its LAN ports and its Wi-Fi connection EDIT: as far as im aware its possible to have the 2nd routers IP Address both INSIDE or OUTSIDE (this method) the DHCP Range of the first modem/router, ive seen advice where both have worked.
as for your TV, it sounds like you are trying to Network them together so you can browse/watch files on your TV from your laptop..right? - your TV would have instructions on how to do this if it uses a specific utility/app supplied with the TV, but normally you would have Homegroup running in Windows 7 and this is what networks the computers together, you would then enable sharing on the folders you want too access via the TV, so in laptop right-click on folder (root folder would give access to all folders and files within) , choose PROPERTIES, then SHARING then ADVANCED SHARING and check 'SHARE THIS FOLDER' and click OK - now any computer connected to the router/network via LAN or WIFI can access this folder by accessing the NETWORK link in Start Menu and using the Homegroup password when prompted - but your TV is specific and will/should have its own instructions, disable password on laptops homegroup, this will make it easier.