I can't think WHY this is happening. However you may be able to configure the old router as an access point and go via that to your existing router. This will split your "long" cable into 2 shorter ones. A thought has struck me: do you need the 25m or is it a coiled up cable? Coiled up cables cause ...
The output of ifup indicates that the router is not responding. The Pi is begging for an IP address but the router is ignoring it. Assuming that the cable is OK (can you try swapping with another?) then I would look to the router. The Pi side of things seems to be Ok to me. I could be wrong and freq...
Some more info will help: If you don't understand any of the terms just ask (or google) 1. Wireless or wired connection? 2. Static or DHCP? 3. When you reboot is it by power off/on or a software reboot? Try running: ifconfig from a terminal window. Do this for both when the network connection works ...