yes, it is called "Daisy Chaining" .. it is possible and works, but is not advisable. If both routers have wireless components the wireless signals could interfer with eachother.
Your best bet would be to get a Switch or Hub to attach to the back of the first router. This will provide you with a non-wireless center that should have more than enough ports for all of your ethernet devices.
Also, please ensure that you do not have a cordless phone base with in 10 feet of your original router, this could interfere with WiFi signals and cause weaker signal strength in outlying computers.
If you are are only 35M away you may want to try a higher end Router. The Net Gear MIMO and N routers would great.
Lots of solutions, hope one works for you.
(I really like Net Gear Products, they are all about the same price.)