Today I had problems with the internet connection so I rebooted the router by pulling the plug and reinserting it.

Since then, I've lost the wifi part of the router. The ethernet side of things work well. I've tried disabling and reenabling the wifi. I've tried different channels and modes. I've done a factory reset and I still can't find it.

Both computers (Win7 and XP) and iPhone 4S cannot see the router. The WLAN light is on. Etherent works fine and posting on here with it.

Is the router broken? Does it need replacing? Is there anything else I can do?

It's likely the router does have a fault but try updating it to 3.6.3 firmware, if that doesn't help, back up your config, factory reset the router and check whether wireless works or not - if it's still not working after doing all of that? definitely faulty

Already updated firmware and tried factory reset.