I am assuming that you are using IP addresses to ping with, and not the hostname (if the latter then you have a hostname resolution issue).
For the former, it is most likely a firewall issue. When Windows
firewall is on (as the default settings) in Windows XP computer, it
will not respond to ping requests, so obviously you can’t ping to the
particular computer. You will be getting ‘Request Time Out’ reply
from the destination, even though its connected and accessible in
local network. The reason behind is that the ICMP packets, which are
used in ping command, are blocked in default firewall rule in Windows
XP. The 'pinging' host sends ICMP packets to the destination and waits
for the response. When the destination computer doesn’t acknowledge or
reply these packets you will be seeing ‘Request time out’ reply.
There are two methods by which you can enable ping, or ICMP
Requests, in XP.
1) Completely switching off the firewall service (This is not
recommended in most cases)
2) Only enable ICMP packets (excepting ICMP packets in Firewall rule),
so while firewall is on ping requests also will work. You can do this
a) Go to Network connections in Control panel;
b) Right Click the connection you want to enable ICMP/Ping requests
(normally local network);
c) Click Properties;
d) Go to Advanced tab and press Settings button under Windows
e) Press Settings button in ICMP area, and finally;
f) Enable the tick in ‘Allow incoming echo…..’. Press OK.
Now this computer will accept ping ICMP echo requests and reply to
By enabling Echo or ICMP or Ping requests by this method without
completely switching off the firewall, the computer will be safe in
network and reply to ping/ICMP requests. That will allow you to
monitor and manage IP address and hosts on your network.
Source: How to enable ping in XP