The previous occupant of your current IP was most probably running a Gnutella client. The fix of course is to get a new IP.

To get a different IP - that's tricky. If it's a PPP connection (dial-up, PPPoE etc) then you should be getting a different IP each time you connect. If it's PPPoA or DHCP - then you'll have to wait until your lease expires. Windows boxen have buggy DHCP clients. Even if you reboot they'll try and get the same IP the next time they connect... if the IP is available a "polite" DHCP server is going to let you have it.

If it IS a DHCP connection you're making, try "breaking" the DHCP renewal chain by specifying your own IP in your TCP/IP properties. Set up the connection to use a static IP in the same /24 you're currently in. (ie, add 1 to your current IP). This won't work of course, but after you specify it, reboot, and then re-configure back to DHCP it forces your Win DHCP client to make a clean renewal request. If that doesn't make sense, just do this:

Configure your TCP to use a static IP.
Reboot.
After the reboot, configure BACK to DHCP.
Reboot.

Now you should have a new address and the probes should stop.