Surely, you can do that! There are several options to do the job. You may disconnect the failed HDD from PC1 and attach to another PC as a slave disk. Beware of Jumper settings. Start the 2nd PC, and try to locate the 2nd HDD from My Computer > Properties > Manage. Generally windows mounts the slave disk automatically. And it shows the disk as a Drive name. Select the drive name and take backups of important data.
If the HDD is totally damaged, I recommend download a 3rd party SW that may help to recover the lost data. Remember, I use the word “may” it depends on how much the HDD is damaged. For more info, please check here.