Hi there,
As you can tell from the title this forum is for questions regarding developing for the Peer-to-Peer Networking infrastructure in Windows. One can certainly try to create a peer-to-peer solution for transferring your files but that is probably not the best solution. This is not really a development related question (unless you really want to write a program to solve this task). However, in case you are having trouble deciding what to do here's a potential solution --
If your Thinkpad and Dell 4600 both have USB ports you can buy a cheap USB flash drive (about $20) and copy the files in batches from the Thinkpad to the Dell. To be safe, you should disable autoplay on your Windows XP computer before plugging the flash drive into your Dell in case there is any malware that takes advantage of autoplay among the files you have copied. You should also scan the files you copy with up to date anti-virus software before accessing any of them (you can get free-trials of anti-virus software in case you don't have any).
If your Thinkpad does not have any USB ports then there is an alternative -- I expect that your notebook is no longer under warranty. If this is the case you can open up the laptop and extract the hard drive. If your Dell 4600 has USB ports (which it ought to) you can acquire an external harddrive enclosure (a 2.5" external enclosure is probably the right size for your notebook's disk and it'll run you about $20) and mount the hard drive in that enclosure. Again, to be safe you should disable autoplay before plugging in the external harddrive and you should then scan the files using up to date anti-virus software before accessing any of them as there may be malware on the old notebook's hard drive.
Good luck,
Eliot