I have an old sony vaio with a 60 gb hard

How "full" is the hard-drive? Perhaps, you could have only a few gigabytes to be "saved".

Click Start
Click My Documents
Click Edit
Click Select All
Right-mouse click on any of the highlighted items.
Click Properties.
Windows will report on the size (megabytes/gigabytes) of all the selected documents and folders.

Perhaps, you can buy 4GB or 8GB or 16GB USB memory-stick,
and manually copy your 'My Documents' files/folders to that memory-stick.

Or, use the "Windows Files and Settings Transfer Wizard" to "collect" all your files & E-mail, and write an "export" file to that memory-stick.

Then, on the "new" computer, run the same Wizard, and "import" from the USB memory-stick onto your new computer.