Yes, you can, but the method will depend upon the nature of the backup and the OS of each computer. What operating system (e.g. Windows version) was on the previous computer and what is on the new computer?  It sounds as though you may already have a backup from the previous computer. What type of backup is it? What application or website do you use for your email?
Can I use a backup from my previous computer to restore documents, emails, etc, to my new Dell? If so, how? For more questions regarding this contests, please visit the Contest Information Page here.
DS 07/19: Can I use a backup from previous computer to restore?