How to verify if your system is connected to the wireless network?

If you run the "ipconfig /all" in a command window, you should get a response like this:

C:>ipconfig /all

Ethernet adapter Wireless Network Connection:

Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : Intel(R) PRO/Wireless
Physical Address. . . . . . . . . : 00-0E-35-BF-DA-58
Dhcp Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
IP Address. . . . . . . . . . . . : 192.168.1.100
Subnet Mask . . . . . . . . . . . : 255.255.255.0
Default Gateway . . . . . . . . . : 192.168.1.1
DHCP Server . . . . . . . . . . . : 192.168.1.1
DNS Servers . . . . . . . . . . . : 192.168.2.1
Lease Obtained. . . . . . . . . . : Thursday, November 30
Lease Expires . . . . . . . . . . : Friday, December 01,

If you run the "ping www.google.com" command in a command window, you should get a response like this:

C:>ping www.google.com

Pinging www.google.com [72.14.203.104] with 32 bytes of data

Reply from 72.14.203.104: bytes=32 time=37ms TTL=241
Reply from 72.14.203.104: bytes=32 time=37ms TTL=241
Reply from 72.14.203.104: bytes=32 time=37ms TTL=241
Reply from 72.14.203.104: bytes=32 time=37ms TTL=241

Ping statistics for 72.14.203.104:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 37ms, Maximum = 37ms, Average = 37ms