try rebooting the device by holding the power on for a full 30 seconds (40 if it's a Fire)
try rebooting the router by unplugging it for a minute
make sure your router i broadcasting in both 2.4 & 5.0Hz (Kindles can't use 5.0Hz)
and btw, no Kindles have been made redundant - my Kindle 2 (2009 model) works just fine and connects wirelessly w/o any problems
if all esle fails, you can talk to Customer Service: if you click on the Help link on the bottom of the page, select Need more help? and then Contact us, you will be able to get some one on one real time help from the UK Customer Service team.