Red x on network icon

This is Vista question, but I usually get better results here. The network icon on my wife's desktop has a red X on it. I right clicked and it ran some kind of diagnostics and supposedly sent a message to MS, who I'll never hear from, I'm sure. My desktop is fine...no red x on my network icon and I'm able to play music files from my desktop on my Samsung smart TV. Do I need to concern myself with this red x?

Normally, a red cross means: no internet access. Is that the case?

Could also be the network adapter is turned off, Wi-Fi is off or the Ethernet cable is unplugged.

No...she can log on to the internet. We don't have ethernet or Wi-Fi adapter. Wireless Wi-Fi. ( I am considering going ethernet due to Netflix and Amazon video rental stopping while a movie is playing).