There are two things happening here:
First, if you are using the headphone out jack of the amp (which it sounds like from your description), the signal level will depend on the volume setting on the amp. There should be a “line-out” socket on the amp - or more usually two sockets, red and white, for left and right - which will give you a proper line-level signal to go into your computer, and it will be independent of the amp volume setting.
Secondly, most laptops only have a mic-in jack, which is looking for a tiny mono signal from a microphone, and you are feeding it a line-level stereo signal from the amp which is overloading it.
That’s because the desktop had a line-in jack, designed to take the high-level stereo output from your amp. Unless you are one of the lucky few whose laptop actually has a jack which is capable of switching from Mic to Line-in (look in Control Panel > Sounds and Audio), your best bet is to get an external USB sound card and plug the output from your amp into it.
Look at this thread:
which has reviews of sound cards which work well with Audacity.
BTW, more detail about your setup might help us help you; model number of your amp? which Sony Vaio? which version of Audacity? (the current version 1.3.11 is recommended for Windows 7). It’s difficult to give us too much detail.
PO’L