There’s a couple of choices, assuming you have a router between your PC and t’internet:-
1. Change the DHCP lease timeout settings in your router’s config to be a very long time. However, at somepoint you may still get a different IP assigned to your PC.
2. The most surefire method is to change your network card to a static IP address rather than DHCP. First, find out your current IP – one that has Azureus etc all working fine. Then get the properties up for your network connection, select “Internet Protocol (TCP/IP), select Properties, and then “Use the following IP address”. Enter the address you had above. You’ll need the subnet mask and gateway addresses too – get these by doing “IPConfig” from a command prompt. The final step to set your primary DNS server address – this will be the local address of your router (i.e. the gateway address).
#2 sounds harder than it is.
If you do have a router, then it does not matter if your ISP gives you a static IP or not.
If you don’t have a router then I would have to do some research to find an alternative. You can probably do what you need via a network bridge – it’s a software thing in XP. But I’m not too familiar with the details.