Don't trust that software or any driver software. They often give strange results and if they offer drivers, more often than not they fail. Some of these driver finder companies require payment for finding and providing drivers which is, in my view, a scam because I have never yet had to pay for drivers.
What router do you have? Make and Model please.
I find it strange that a router driver failed and the Netgear Support couldn't tell you what to do next. May be another call to them? You may get a different person who can explain better. Are you using the same router to connect to the internet on the computer you used to post your message? If so, then the router doesn't sound faulty to me.
On the laptop where the wireless connection fails, are you using a wireless adapter now, or does this laptop have it's own wireless network card?
Any error messages about this connection failure? And can you head over to the Device Manager, (assuming you are using Windows), and see if there are any errors reported with the system's hardware?
I have a Gateway M2624u laptop. Recently I have not been able to connect to my wireless router. I called the help desk for Netgear and after a long and frustrating session the tech informed me that it had something to do with the internal driver, Windows couldn't update it and I needed to buy an external adapter.
I ran DriverDoc to see what else was wrong; report showed 5 drivers are out of date:
Ralink Wireless LAN Driver
Ralink RT2870 USB Wireless LAN card driver
Marvell Yukon Ethernet Controller Drivers
AMD Catalyst Mobility Display Driver
Realtek ATI HDMI Audio Driver