I am trying to set up a simple wired Ethernet network between two pcs
running windows XP SP2 . One computer (Laptop) is XP Home Edition and
the other (Desktop) is XP Media Center Edition. It's the first time I
have done this, so forgive me if I am giving too much or too little
information.

I have a crossover Ethernet cable connected between the two Ethernet
cards in both machines. There are no routers, switches, or hubs used.

When I click on the My network places, I just see a shared folder for
my local computer and I don't see the other computer.

When I click on the view network connections, I see my Ethernet
connection, and the state is "Limited or no Connectivity". There is
a little yellow triangle with an exclamation mark above the icon. If I
click "repair" a window pops up saying that it's trying to renew
the IP address, and after about a minute a window pops up and says it
failed to do this and to contact the network administrator.

If I click on properties for the Ethernet connection I see the
following items listed and checked:

Client for Microsoft Networks
File and Print sharing for Microsoft Networks
QoS packet Scheduler
TCP/IP

The properties for TCP/IP are "Obtain an IP address automatically"
and "Obtain DNS server address automatically".

The configuration I described so far is true for both computers.

Each computer has a different computer name, but they are both part of
the MSHOME Workgroup.

I have the firewall software disabled on both computers.

I have rebooted both computers several times.

I think I might be missing something very easy. Any ideas?

Here are the ipconfig /all results:

--------------------------
For the DESKTOP PC:

Windows IP Configuration
Host Name . . . . . . . . . . . . : hp1
Primary Dns Suffix  . . . . . . . :
Node Type . . . . . . . . . . . . : Hybrid
IP Routing Enabled. . . . . . . . : No
WINS Proxy Enabled. . . . . . . . : No

Ethernet adapter Local Area Connection:
Connection-specific DNS Suffix  . :
Description . . . . . . . . . . . : Realtek RTL8139/810x Family Fast
Ethernet NIC
Physical Address. . . . . . . . . : 00-13-D4-98-D7-6E
Dhcp Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
Autoconfiguration IP Address. . . : 169.254.9.192
Subnet Mask . . . . . . . . . . . : 255.255.0.0
Default Gateway . . . . . . . . . :

PPP adapter The Internet (1):
Connection-specific DNS Suffix  . :
Description . . . . . . . . . . . : WAN (PPP/SLIP) Interface
Physical Address. . . . . . . . . : 00-53-45-00-00-00
Dhcp Enabled. . . . . . . . . . . : No
IP Address. . . . . . . . . . . . : 172.165.159.125
Subnet Mask . . . . . . . . . . . : 255.255.255.255
Default Gateway . . . . . . . . . : 172.165.159.125
DNS Servers . . . . . . . . . . . : 205.188.146.145
NetBIOS over Tcpip. . . . . . . . : Disabled

--------------------
and for the LAPTOP PC:

Windows IP Configuration
Host Name . . . . . . . . . . . . : TOSHIBA1
Primary Dns Suffix  . . . . . . . :
Node Type . . . . . . . . . . . . : Unknown
IP Routing Enabled. . . . . . . . : No
WINS Proxy Enabled. . . . . . . . : No

Ethernet adapter Local Area Connection:
Connection-specific DNS Suffix  . :
Description . . . . . . . . . . . : Intel(R) PRO/100 VE Network
Connection
Physical Address. . . . . . . . . : 00-00-39-23-A6-DA
Dhcp Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
Autoconfiguration IP Address. . . : 169.254.221.242
Subnet Mask . . . . . . . . . . . : 255.255.0.0
Default Gateway . . . . . . . . . :

Ethernet adapter Local Area Connection 2:
Connection-specific DNS Suffix  . :
Description . . . . . . . . . . . : WAN Network Driver
Physical Address. . . . . . . . . : 00-03-8A-00-00-11
Dhcp Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
Autoconfiguration IP Address. . . : 169.254.101.152
Subnet Mask . . . . . . . . . . . : 255.255.0.0
Default Gateway . . . . . . . . . :  

Thanks.