HELP! My network and internet seem to be collapsing...

I am having trouble with my network and internet access. My Verizon-provided router goes out at random moments. If it resets and all lights come up, sometimes it works, sometimes it doesn’t.

And my wireless network connection icon has disappeared from my tray so I can’t fix whatever is wrong and I can’t talk to my laptop.

But even odder, when the router has all its lights on I can go to sites like fluther but I can’t upload. [Right now I am at my laptop which is temporarily on another network to upload this.] On my desktop I can’t access the tray icon to switch to the other network.