|You can't use two routers in the same network setup connected to the same internet account.|
You would have to subscribe to a new internet account if you want to be able to use your own router independently of the existing one.
If you just want a stronger wireless signal using the existing internet account you need to install a "wireless range extender" (also called a wireless repeater) like the three shown at top of this page: http://www.amazon.co.uk/wireless-re...
The range extender does not replace the existing router. It sits between the existing router and your PC to boost the router's wireless range.