You have multiple Windows XP machines on an internal network (same external IP address, I presume) and you find that one of these machines sees slower connections to one-specific external site.
If this is your exact description,
It is very likely a problem on this internal Windows XP machine.
It is unlikely to be a problem in your internal network -- because,
that should cause all connectivity to have problems.
To check your Internet connectivity in general, you could something like SpeedTest from this machine and one other that seems to work fine. But, if the problem is specifically with just one site, this would not show different results.
To verify that your internal network path is good you could '
ping' the router's internal address from this machine and one another that works fine -- to compare results.
You could also 'flood ping' to see continuity. But, again, since you are facing problems with a single site on this single internal machine, it is very likely a problem with the internal machine's software state.
To get deeper in such analysis (when you have run out of all configuration differences between this machine other working machines), you would want to take packet captures (Wireshark) on two machines while accessing the site in question and compare them to see what is going wrong with the problem machine.