You could try adding all your log files to a .ZIP file. then sending the .ZIP file as an attachment from your hotmail address to Your same hotmail address. This will place the attachment online in your inbox (By Just sending the mail to yourself), accessible from another computer by logging into your hotmail account on the web
If the .ZIP files become too large for sending you can always attach .ZIP's to more e-mails until all log files are available.
This is only asuming the other computer will have internet connection
There is also no need for programes, you can buy a CD-R blank disk to add your files which need transfering. Floopy disks are also good, but are insufficient in space.
I hope that helps