If your images were stored by reference, you have a number of options. One is copy the folder of images over to your new computer and then use Replace Field Contents with a calculation that updates the existing file path in the container field to a new valid file path to the new location. This treats the container field as though it were a text field instead of a container field in your use of replace field contents.
Another option would be to set up a looping script on your old computer that loops through all the records and uses export field contents to export each file to the temporary folder and then re-inserts them without specifying the Store a reference option. You then copy over the file with it's embedded images and use a similar script to reverse the process by exporting the images to the desired location and then re-inserts them "by reference" from the new location. Or you can change the storage option to "external" if you have at least Filemaker 12 and not use "by reference" images.
I'd go with the first option if there are a large number of images and the second if the number is relatively small.
For more on File Paths, container fields and the script steps that can work with them, see: Exploring the use of a $Path Variable in Scripts