On the 'Old' computer, you may be able to locate your Serial Number for LR3- Look in-
C:\ProgramData\Adobe\Lightroom\Lightroom 3.0 Registration.lrreg
Or if you have the Serial Number on a box or written down somewhere, that is also suitable.
You can download v3 from this site-
a v3 Serial Number will allow you to install v3.6. (The latest version available for a v3 licence.)
Run the downloaded program that will install and ask for your Serial Number.
You will need to copy over all your image files and Lr Catalogs- Do some research on the method required-