Method 1: rename drives and directories on your new computer so that the path to your photos is the same.
Method 2: Use a script to update all your paths in all your containers to point to the new location.
To see the paths actually stored in your container fields, create a calculation field set to return text and enter the name of the container field as its expression.
Once you understand how to update the paths in each record you can use a script something like this:
Show All records
Replace Field Contents [No dialog; yourtable::yourcontainer field; <Your text expression to modify the path>]