I tried to ping my desktop's IP address from my laptop. 4 packets sent, none received.
Even though the two computers are on the same network, same router, etc., they can't see each other.
That's a huge clue that they may not be on the same network (unless your router is configured to not respond to pings).
Type ipconfig /all on each machine and compare. They both must have the same network address and have the same net mask. The default gateway, dhcp and dns servers should be the same on both and point to the router if they are both connected to the router.
Windows IP Configuration
Host Name . . . . . . . . . . . . : main
Primary Dns Suffix . . . . . . . :
Node Type . . . . . . . . . . . . : Unknown
IP Routing Enabled. . . . . . . . : No
WINS Proxy Enabled. . . . . . . . : No
Ethernet adapter Local Area Connection:
Connection-specific DNS Suffix . :
Description . . . . . . . . . . . : Realtek RTL8139/810x Family Fast Eth
ernet NIC
Physical Address. . . . . . . . . : 00-30-1B-B9-CF-06
Dhcp Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
IP Address. . . . . . . . . . . . : 192.168.1.3
Subnet Mask . . . . . . . . . . . : 255.255.255.0
Default Gateway . . . . . . . . . : 192.168.1.1
DHCP Server . . . . . . . . . . . : 192.168.1.1
DNS Servers . . . . . . . . . . . : 192.168.1.1
Lease Obtained. . . . . . . . . . : Monday, August 17, 2009 8:09:46 PM
Lease Expires . . . . . . . . . . : Tuesday, August 18, 2009 8:09:46 PM