Photoshop Elements is an Adobe product and if it was pre-installed on your Sony Vaio then usually these are trial versions or limited versions of the full Adobe software.
Software applications don't transfer well in Windows from one computer to another. The files that are installed during the setup procedure are placed all over the operating system and specific entries made in the Windows Registry and that makes hunting them down to copy them over nigh on impossible.
In any case, OEM versions of software are fixed to the machine they came on, so even if you could transfer the files and registry entries across, the license activation would fail.
Sorry, but it doesn't look hopeful.
Just curious if there's any way to transfer the photoshop elements included with sony vaio laptops? Is there any way to find the product number? Thanks