From what you said, sounds like you used the Mint4Win option on your last laptop vs. a real installation of Mint. If you are planning to use Mint as the primary OS and only use Windows 8 for certain special programs on your new laptop, then you're better off doing a regular install of Mint -- not a Mint4Win install within Windows.
pointed out, you will need to shrink the Windows partition to make room for Mint. Also, as he stated, use Mint 16 (or 13, 14 -- but not 15; support for 15 ends this month). Assuming you have Windows already installed back on the drive, you need to first determine which version is installed (the 32bit or 64bit version) and whether or not it was installed under UEFI or Legacy/CSM/BIOS boot mode.
Use this resource to make that determination for certain (don't guess or assume you know): http://www.rodsbooks.com/refind/bootmode.html
. Scroll down to the section "Identifying Your Windows Boot Mode" and follow the instructions.
If the results from that determine that Windows was installed in UEFI mode, then absolutely recommend reading the link computerbob
referred you to above before you proceed. Read more than once if necessary. That will give you a much better idea on how to proceed with install.