Our wireless network has been running strong for quite some time. When people have trouble connecting it is usually due to a small hardware glitch on their machine. These things generally work themselves out when I make sure they are set up to be automatically assigned an IP address (Properties of the wireless connection -> General Tab ->Properties of Internet Protocol (TCP/IP)). If this doesn’t work, an attempt to release and renew the IP address that the computer is trying to use often does the trick (Start -> Run -> cmd -> ipconfig /release (and then ipconfig /renew)).
Once I’ve gone through these steps, the internet connection must be tested to see if they had any effect. Pinging a site out on the web (Start -> Run -> cmd -> ping URL) would be a fine and dandy way to test the internet connection, but I bet people get a better idea that the connection is indeed working when they see a browser launch and their homepage appear. Also, and there is only a slim chance of this happeneing, but perhaps pinging would work but the browser would still act up. Unlikely, yes, but one never knows.
The only reason that opening their browser is not a good option is because it is a small invasion of their privacy. Before double clicking, I make sure to ask their permission. Their blessing on my action notwithstanding, I still feel awkward throughout the end of the transaction.
Am I overreacting?