Why do I not see the Airplay icon on any device?

Question

Hello everyone
None of my Apple devices show the Airplay icon anymore.  The devices I have are :
*  Apple TV 2nd Gen (MC572B/A - v5.3)
*  MacBook Mid 2007 13-in running OS X Lion 10.7.5
*  MacBook Late 2009 13-in running OS X Mountain Lion 10.8.4
*  2x iPhone 4S (both running iOS 6.1.3)
Other non-Apple devices are 2x 2013 Amazon Kindles, a PS3, Sky HD+ Box w/Wireless Receiver.
I received my Apple TV in Christmas 2011 and I had not noticed a problem with Airplay until I got Sky in February 2013.  My network was running on WEP connection as both of the MacBooks had problems using WPA/WPA2 connections when initially setting up the Wifi a couple of years before.  It turned out that the Sky box would only play with a WPA connection.  It's from here that Airplay stopped working.  Previously we could use everything associated with Airplay - stream music from all devices, send pictures and video, and also stream content from iTunes to the Apple TV including films and TV Programmes.  Our Apple devices can now connect to the Internet using a WPA connection (the 2007 MacBook cycles for a long time but that is another issue) so this is not a problem, and it's worth noting that all of my non-Apple devices work absolutely perfectly and always have done (also including previous smartphones etc).
I have tried the following solutions :
*  http://support.apple.com/kb/ts4215 (Troubleshooting AirPlay and AirPlay Mirroring);
*  Changing the DNS Servers (Unsuccessful);
*  Restarting the Router (AirPlay icon showed for less than 15 minutes before disappearing again);
*  Restarting Apple TV (Unsuccessful);
*  Toggling AirPlay in Apple TV (Unsuccessful);
*  Deleting the WiFi network in Apple TV (Unsuccessful);
*  Deleting the WiFi network on my 2007 MacBook and manually adding it (Unsuccessful);
*  Deleting the WiFi network on both iPhone 4S' (Unsuccessful);
*  Removing the Firewall from my router (Unsuccessful);
*  Changing the security options on my router (Unsuccessful);
*  Powering off all devices and back on (Unsuccessful);
*  NOTE : Home Sharing is turned ON and is visible on Apple TV;
What else can I try that isn't listed?  A follow up question is if I bought an Airport Express (I don't want to tbh), would that immediately solve the lack of AirPlay and cycling issues?
Thanks in advance

Answer 1

Just to finish this discussion off, the issue was 100% the router firmware.  Please see the below, direct from the support pages of www.plus.net :
The  585v8 v8.2.7.7 firmware is known to cause wi-fi connectivity problems with certain Apple computers. To fix this problem we recommend that you upgrade to v8.2.7.8 that features updated wi-fi drivers from the chipset manufacturer. No official upgrade tool exists for Apple computers so you may need to reflash the firmware using a Windows computer instead.
I did this yesterday after borrowing a PC and it fixed all of the issues I was having - no Airplay icons, cycling for wifi networks, dropped connections - all of these righted themselves after a firmware update.
The reason it wasn't the first thing tried was that I was under the impression that a) my router had up to date firmware as it wasn't clear on my ISP's website, and b) that my router firmware would have updated automatically as there was no option to update on my routers settings page.
The WEP security issues were a bit of a red herring tbh.  When I first joined my ISP downgrading the security was the advice given after I experienced initial connection problems, but this was probably due to a lack of updated firmware at the time - the issues had to be related to security which would have been solved by an open network.  Obviously this is not ideal, so a WEP connection was a wobbly middle ground.
Thanks for everyone's help.