The Ubuntu partitions will be ext4, so you won't be able to see them on Windows. There is some software you can use to read ext4, but I have never found anything that worked satisfactorily. Your best chance is probably using a Linux live USB drive. Instructions for creating one with Ubuntu can be found here. Boot using the USB stick, and select the option to try Ubuntu without installing. Then you should be able to use Ubuntu's file manager/terminal to copy files from your old disk.