Are you using wpa encryption? If so, use wpa_cli to montitor whether the device is losing it's association frequently. Also check whether you have the default gateway set to 192.168.1.1 and if you have the nameserver (DNS) addresses. Also see if you can browse to the routers setup. You will first need to allow that with a wired connection however I wouldn't recommend it if you don't use encryption or just use WEP. If you have a second device such as a NIC device, make sure it either isn't on the same subnet or is shut down.
You can check the route with the /sbin/route command.
Here is how mine looks like:
Kernel IP routing table
Destination Gateway Genmask Flags Metric Ref Use Iface
192.168.1.0 0.0.0.0 255.255.255.128 U 0 0 0 wlan0
192.168.1.128 0.0.0.0 255.255.255.128 U 0 0 0 eth0
169.254.0.0 0.0.0.0 255.255.0.0 U 0 0 0 eth0
127.0.0.0 0.0.0.0 255.0.0.0 U 0 0 0 lo
0.0.0.0 192.168.1.1 0.0.0.0 UG 0 0 0 wlan0
My eth0 device is connected to a switch with a networked printer. Notice that it is on a different subnet.
The last line is the default gateway. If it isn't present, then you can set it with:
"sudo /sbin/route add default netmask 255.255.255.0 gw 192.168.1.1 wlan0"
I'm assuming that you don't have your network subnetted.
Cat out the /etc/resolv.conf file. The nameservers listed should match what the route says on its status page. They are needed to resolve domain names to IP address on the internet.